SEARCH · Engineering Papers

Results for “oscillators”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

All sources NASA NTRS DOE OSTI

DOE OSTI2020

Measurement of 3-Flavour Neutrino Oscillation Parameters in the NOvA Experiment

NOvA is a long-baseline neutrino oscillation experiment consisting of two functionally identical tracking calorimeters, a Near and Far Detector, that measure neutrino interactions induced by the Fermi National Accelerator Laboratory’s NuMI beam at baselines of 1 km and 810 km, respectively. The NuMI beam can be configured to produce either a primary ν µ neutrino or $\bar{ν}$ µ anti-neutrino beam. Neutrino oscillations are observed and measured by the analysis of ν µ + $\bar{ν}$ µ disappearance and νe + $\bar{ν}$ e appearance in the beam, comparing the neutrino energy spectra in the Near and Far detectors means that neutrino oscillation parameters sin 2 θ 23 , |Δ$m^2_{32}$|, and δ CP can be constrained. This thesis presents the 2018 NOvA ν µ +$\bar{ν}$ µ disappearance, ν e +$\bar{ν}$ e appearance, and combined analyses using both neutrino and anti-neutrino data, where oscillation fits have been performed, where possible, on an event-by-event basis rather than on a bin-by-bin basis as has conventionally been used in NOvA oscillation analyses. This allows for better precision in applying both neutrino oscillation probabilities and systematic uncertainties. Furthermore, oscillation analyses for the disappearance, appearance, and combined channels are presented using an unbinned likelihood fit and compared with the equivalent binned χ 2 likelihood fit used in the standard analysis. The 14 ktonne detector equivalent beam exposures used for this thesis are 8.85 × 10 20 and 6.91 × 10 20 protons on target for neutrino and antineutrino data respectively, corresponding to 5 years of NOvA data taking. A combined ν µ + $\bar{ν}$ µ disappearance and ν e + $\bar{ν}$ e appearance fit to the Far Detector data, assuming normal mass ordering and using the event-by-event oscillation and unbinned fitting methodologies, produces oscillation parameter constraints of Δ$m^2_{32}$ = (2.50$^{+0.08}_{-0.06}$) × 10 -3 eV 2 , sin 2 θ 23 = 0.59$^{+0.02}_{-0.04}$, and δ CP = 0.72$^{+0.5}_{-0.9}$π.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Constructing Data-Driven Predictions at the Far Detector for NOvA's Neutrino Oscillation Analysis.

NOvA, is a two-detector, long-baseline neutrino oscillation experiment located at Fermilab, Batavia, IL, USA. It is designed primarily to constrain neutrino oscillation parameters using $\nu_\mu \ (\bar{\nu}_\mu)$ disappearance and $\nu_e \ (\bar{\nu}_e)$ appearance data. The Neutrinos at Main Injector (NuMI) beamline at Fermilab provides a high purity 900 KW intense beam of neutrinos and anti-neutrinos to NOvA. The NOvA Near Detector, located 100m underground and 1km away from the beam source, observes the un-oscillated $\nu_\mu \ (\bar{\nu}_\mu)$ and beam $\nu_e \ (\bar{\nu}_e)$ event spectrum. The Far Detector, located in Ash River, MN, USA, is 809 km from the ND and records the oscillated $\nu_e \ (\bar{\nu}_e)$ and the un-oscillated $\nu_\mu \ (\bar{\nu}_\mu)$ event spectrum. NOvA uses a data-driven technique called extrapolation to predict the expected number of $\nu_\mu \ (\bar{\nu}_\mu)$ and $\nu_e \ (\bar{\nu}_e)$ events at the Far Detector using the Near Detector data. The use of data from a functionally equivalent Near Detector provides a powerful constraint on the systematic uncertainties in NOvA neutrino oscillation analyses. As NOvA continues to add data statistics, a robust constraint on systematics becomes more crucial for neutrino oscillation analysis. The details of the NOvA neutrino oscillation analysis framework and how it constrains dominant systematic uncertainties using the Near Detector data will be discussed in this poster.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Latest Three-Flavor Neutrino Oscillation Results from NOvA

NOvA, is a two-detector, long-baseline neutrino oscillation experiment located at Fermilab, Batavia, IL, USA. It aims to constrain neutrino oscillation parameters by analyzing $\nu_\mu (\bar{\nu}_\mu)$ disappearance and $\nu_e (\bar{\nu}_e)$ appearance data. The experiment uses the Neutrinos at Main Injector (NuMI) beamline at Fermilab, which delivers a high-purity 900 KW beam of neutrinos and anti-neutrinos. The detectors are functionally identical finely granulated liquid tracking calorimeters, both situated 14.6 mrad off-axis to the beam direction. The NOvA Near Detector (ND), situated 100 meters underground and 1 kilometer from the beam source, detects the un-oscillated $\nu_\mu (\bar{\nu}_\mu)$ and beam $\nu_e (\bar{\nu}_e)$ events. The Far Detector (FD), located in Ash River, MN, USA, 809 kilometers from the ND, records the oscillated $\nu_e (\bar{\nu}_e)$ and the un-oscillated $\nu_\mu (\bar{\nu}_\mu)$ events. NOvA employs an extrapolation technique to predict the expected events at the Far Detector based on the Near Detector data, thereby providing a significant constraint on systematic uncertainties in the oscillation analyses. As NOvA accumulates more data, controlling these systematic uncertainties becomes increasingly important. This talk will detail the NOvA neutrino oscillation analysis framework and its approach to minimizing dominant systematic uncertainties using Near Detector data. The latest three flavor neutrino oscillation results based on a neutrino-beam exposure of $26.60 \times 10^{20}$ POT and an anti-neutrino beam exposure of $12.50\times 10^{20}$ POT and a novel low energy $\nu_e$ sample, will also be presented.

Choudhary, Brajesh↗

DOE OSTI2021

Testing the reliability of interpretable neural networks in geoscience using the Madden–Julian oscillation

Abstract. We test the reliability of two neural network interpretation techniques, backward optimization and layerwise relevance propagation, within geoscientific applications by applying them to a commonly studied geophysical phenomenon, the Madden–Julian oscillation. The Madden–Julian oscillation is a multi-scale pattern within the tropical atmosphere that has been extensively studied over the past decades, which makes it an ideal test case to ensure the interpretability methods can recover the current state of knowledge regarding its spatial structure. The neural networks can, indeed, reproduce the current state of knowledge and can also provide new insights into the seasonality of the Madden–Julian oscillation and its relationships with atmospheric state variables. The neural network identifies the phase of the Madden–Julian oscillation twice as accurately as a linear regression approach, which means that nonlinearities used by the neural network are important to the structure of the Madden–Julian oscillation. Interpretations of the neural network show that it accurately captures the spatial structures of the Madden–Julian oscillation, suggest that the nonlinearities of the Madden–Julian oscillation are manifested through the uniqueness of each event, and offer physically meaningful insights into its relationship with atmospheric state variables. We also use the interpretations to identify the seasonality of the Madden–Julian oscillation and find that the conventionally defined extended seasons should be shifted later by 1 month. More generally, this study suggests that neural networks can be reliably interpreted for geoscientific applications and may thereby serve as a dependable method for testing geoscientific hypotheses.

58 GEOSCIENCES↗

DOE OSTI2021

Tuned oscillator atomic force microscopy methods and apparatus

Techniques for operating an atomic force microscope, the atomic force microscope comprising a cantilever and configured to image a surface of a sample using a probe tip coupled to the cantilever, the techniques comprising using a controller to perform: obtaining, based on at least one intrinsic parameter of the cantilever, a first quality factor and a first free oscillation amplitude, wherein the cantilever exhibits only one stable oscillation state when oscillating at the first free oscillation amplitude and operating at the first quality factor; and controlling the cantilever to exhibit the only one stable oscillation state by controlling the cantilever to oscillate at a fixed frequency at or near a resonance frequency of the cantilever, oscillate at the first free oscillation amplitude, and operate at the first quality factor.

Schwarz, Udo↗

DOE OSTI2023

Oscillator for adiabatic computational circuitry

An adiabatic resonator, an adiabatic oscillator, and an adiabatic oscillator system are disclosed. An adiabatic system is one that ideally transfers no heat outside of the system, thereby reducing the required operating power. The adiabatic resonator, which includes a plurality of tank circuits, acts as an energy reservoir, the missing aspect of previously attempted adiabatic computational systems. By using the adiabatic resonator as a feedback element with an amplifier, an adiabatic oscillator is formed. An adiabatic oscillator system is formed with a primary adiabatic oscillator feeding a plurality of secondary adiabatic oscillators. In this manner, the adiabatic oscillator system may be used to generate the multiple clock signals required of adiabatic computational logic elements, such as Split-level Charge Recovery Logic and 2-Level Adiabatic Logic. The adiabatic oscillator system stores enough energy to drive many individual adiabatic computational logic elements, permitting implementation of complex logic circuits.

Brocato, Robert W.↗

DOE OSTI2020

Flow-induced oscillation patterns for two tandem cylinders with turbulence stimulation and variable stiffness and damping

Herein, the oscillation patterns of two 1-DOF cylinder oscillators, undergoing VIV and galloping, are investigated in a free surface water channel for 3.2 × 104 ≤ Re ≤ 1.2 × 10 5 . The cylinders are arranged in tandem and supported by springs for a range of different spring stiffness and damping parameters. The efficiency of a current energy converter (CEC), based on flow-induced oscillation (FIO) of multiple cylinders in tandem, is critically related to the cylinder oscillation patterns. Due to the limited number of studies on the FIO for multiple cylindrical or prismatic bodies, their oscillation patterns have neither been identified nor classified. The surfaces of the cylinders are modified by turbulence stimulation to enhance FIO. Three different center-to-center spacing, five stiffness, and six damping ratios, for a total of 90 sets of experiments were conducted. The current velocity range is from 0.34 m/s to 1.32 m/s. From more than 2000 tests, five major patterns, nine sub-patterns are identified and classified. The patterns are defined based on the amplitudes, frequencies and the phase angle differences between the two cylinders. The characteristics and mechanics of each oscillation pattern are explored and explained from the perspective of fluid-structure interaction (FSI). By systematically varying the parameters, the underlying hydrodynamic mechanisms, including the coupling level between vortices and cylinders, the shielding effect, the wake effect, and the stability states are revealed. Few preliminary observations on the connection between oscillation pattern and harnessed power by the tandem cylinders are reported.

42 ENGINEERING↗

DOE OSTI2024

Forced Oscillation Source Location in Power Systems Using MVMD-assisted DEF in TF Plane

Fast and accurate forced oscillation source location (FOSL) is critical for mitigating forced oscillations in power systems. Here, to overcome the shortcomings of traditional dissipating energy flow (DEF) in decomposing the forced oscillation components from the measurement responses, a multivariate variational mode decomposition (MVMD)-assisted FOSL is proposed in this paper to locate the forced oscillation sources from measurements in time-frequency (TF) plane. The multi-channel measurement matrix of each generator is formed, then the multi-channel modes are decomposed from the formed multi-channel measurement matrix using the MVMD. Further, the intrinsic mode functions (IMFs) associated with the forced oscillation mode are distinguished from the decomposed modes according to the relative energy weights. With the distinguished IMFs, the MVMD-assisted DEF calculation method is developed to locate the forced oscillation source. Finally, the performance of the proposed method is evaluated using the simulation data of the WECC 179-bus test system and IEEE-NASPI Oscillation Source Location Contest as well as the actual PMU data of ISO New England. The results validated the effectiveness and accuracy of the proposed method in the FOSL.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Injection Locking of Gigahertz‐Frequency Surface Acoustic Wave Phononic Crystal Oscillator

Low-noise gigahertz (GHz) frequency sources are essential for applications in signal processing, sensing, and telecommunications. Surface acoustic wave (SAW) resonator-based oscillators offer compact form factors and low-phase noise due to their short mechanical wavelengths and high-quality (Q) factors. However, their small footprint makes them vulnerable to environmental variation, resulting in their poor long-term frequency stability. Injection locking is widely used to suppress frequency drift of lasers and oscillators by synchronizing to an ultra-stable reference. Here, injection locking of a 1-GHz SAW phononic-crystal oscillator is demonstrated, achieving 40-dB phase noise reduction at low offset frequencies and unperturbed low noise at large offset frequencies. Compared to a free-running SAW oscillator, which typically exhibits frequency drifts of several hundred hertz over minutes, the injection-locked oscillator reduces the frequency deviation to below 0.35 Hz. The locking range and oscillator dynamics is also investigated in the injection pulling region. The demonstrated injection-locked SAW oscillator could find applications in high-performance portable telecommunications and sensing systems.

injection locking↗

DOE OSTI2021

Synergistic data analytics for electromechanical oscillation in electric power systems

Accurate real-time estimation of the four electromechanical oscillation properties, i.e., dominant oscillation modes, mode shapes, participation factors, and coherent groups, is of great importance to assess and mitigate potential electromechanical oscillations in interconnected power systems. While eigenvalue analysis can realize such estimation, it requires precise linearized dynamic models and accurate parameters, which are highly difficult to obtain in practice. Data fusion-based modal estimation methods can extract the properties of electromechanical oscillations from measurement data without the power system model and parameters, but most of the time only one or two property assessments can be accomplished each time. To overcome this challenge, this paper presents a synergistic data analytics solution to characterize the dynamic behaviors of electromechanical oscillations from real-time measurement data. Here, the proposed method uses optimized variable projection, and it is capable of estimating all four electromechanical oscillation behavior properties from measured responses. Case studies are performed using the simulated measurement data of a 16-generator 68-bus test system and the field measurements collected by the PMUs deployed in the Yunnan Power Grid. The results demonstrate that the proposed synergistic data analytics solution can achieve satisfactory performance in capturing the properties of electromechanical oscillations from measurement data and exhibit strong robustness against measurement noise when compared with existing measurement-based methods.

42 ENGINEERING↗

DOE OSTI2023

Eastern Interconnection Wide-Area Oscillation Assessment and Study Report

To meet the government mandates such as Renewable Portfolio Standards (RPS), conventional synchronous generators with rotating mass are being displaced by inverter-based resources (IBRs), leading to high penetration of renewable energy sources (RES). As a result, the inherent properties and characteristics of the transformed generation mix may significantly impact the grid behaviour, and it is of paramount significance that the impact and the consequences of the resource mix change is thoroughly understood to adopt measures to maintain reliable grid operations. Of great concern is the inter-area low-frequency oscillation, which usually propagates through a large region and has a system-wide impact. Such oscillations may lead to unnecessary or inadvertent tripping of generators, that may be simply reacting to the oscillation originating from geographically remote sites. Such tripping of generators can lead to cascading outages, system split and load loss events. Over the years, several system-wide oscillation events have been observed across all three North American interconnections. This project titled Wide-area Oscillation Assessment and Trending Study, sponsored by the Office of Electricity (OE) of the Department of Energy (DOE), aims to conduct the required research to capture and investigate the potential changes in wide-area oscillatory performance of the system as a result of resource mix transition. The Pacific Northwest National Laboratory (PNNL) conducted this research and technical staff of Federal Energy Regulatory Commission (FERC) served as advisors to the project. The primary objective of this study is to assess whether there are significant trends in the power system wide-area oscillatory behaviours, as a result of the generation-mix changes due to the increased penetration of RES in the U.S. Eastern Interconnection (EI). The analysis presented in this report can serve as reference for future grid planning and operation of the EI system. This research conducted in this project evaluates the wide-area oscillatory behaviour of the EI, using a model-based approach for potential future resource mixes, and the measurement-based analysis with 21-month phasor measurement unit (PMU) time series. The oscillation modes in EI system along with the impact of the changes of the generation mix on the frequency and damping ratio (DR) of the oscillations have been studied.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Chemical pumps and flexible sheets spontaneously form self-regulating oscillators in solution

The synchronization of self-oscillating systems is vital to various biological functions, from the coordinated contraction of heart muscle to the self-organization of slime molds. Through modeling, we design bioinspired materials systems that spontaneously form shape-changing self-oscillators, which communicate to synchronize both their temporal and spatial behavior. Here, catalytic reactions at the bottom of a fluid-filled chamber and on mobile, flexible sheets generate the energy to “pump” the surrounding fluid, which also transports the immersed sheets. The sheets exert a force on the fluid that modifies the flow, which in turn affects the shape and movement of the flexible sheets. This feedback enables a single coated (active) and even an uncoated (passive) sheet to undergo self-oscillation, displaying different oscillatory modes with increases in the catalytic reaction rate. Two sheets (active or passive) introduce excluded volume, steric interactions. This distinctive combination of the hydrodynamic, fluid–structure, and steric interactions causes the sheets to form coupled oscillators, whose motion is synchronized in time and space. We develop a heuristic model that rationalizes this behavior. These coupled self-oscillators exhibit rich and tunable phase dynamics, which depends on the sheets’ initial placement, coverage by catalyst and relative size. Moreover, through variations in the reactant concentration, the system can switch between the different oscillatory modes. This breadth of dynamic behavior expands the functionality of the coupled oscillators, enabling soft robots to display a variety of self-sustained, self-regulating moves.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Emergent microrobotic oscillators via asymmetry-induced order

Abstract Spontaneous oscillations on the order of several hertz are the drivers of many crucial processes in nature. From bacterial swimming to mammal gaits, converting static energy inputs into slowly oscillating power is key to the autonomy of organisms across scales. However, the fabrication of slow micrometre-scale oscillators remains a major roadblock towards fully-autonomous microrobots. Here, we study a low-frequency oscillator that emerges from a collective of active microparticles at the air-liquid interface of a hydrogen peroxide drop. Their interactions transduce ambient chemical energy into periodic mechanical motion and on-board electrical currents. Surprisingly, these oscillations persist at larger ensemble sizes only when a particle with modified reactivity is added to intentionally break permutation symmetry. We explain such emergent order through the discovery of a thermodynamic mechanism for asymmetry-induced order. The on-board power harvested from the stabilised oscillations enables the use of electronic components, which we demonstrate by cyclically and synchronously driving a microrobotic arm. This work highlights a new strategy for achieving low-frequency oscillations at the microscale, paving the way for future microrobotic autonomy.

42 ENGINEERING↗

DOE OSTI2024

Three-flavor, full momentum space neutrino spin oscillations in neutron star mergers

In the presence of anisotropic neutrino and antineutrino fluxes, the quantum kinetic equations drive coherent oscillations in neutrino helicity, frequently referred to as spin oscillations. These oscillations depend directly on the absolute mass scale and Majorana phase, but are usually too transient to produce important effects. In this paper we present a full momentum-space analysis of Majorana neutrino spin oscillations in a snapshot of a three-dimensional neutron star merger simulation. We find an interesting angular dependence that allows for that resonant and adiabatic oscillations to occur along specific directions in a large volume of the merger remnant. The solid angle spanned by these directions is extremely narrow in general. We then analyze spin transformation in the presence of flavor transformation by characterizing how the effect's resonance and timescale change during a fast flavor instability. For this analysis, we derive a generalized resonance condition that poses a restrictive requirement for resonance to exist in any flavor channel. Finally, we determine that spin oscillations at all locations in the merger snapshot have a length scale that is too large for significant oscillations to be expected even where there exist resonant and adiabatic directions.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Observation of Synchronization between Two Quantum van der Pol Oscillators in Trapped Ions

Synchronization is a hallmark of collective behavior that emerges when nonlinear systems interact, spanning scales from mechanical oscillators to planetary orbits. As a universal phenomenon, it underpins the study of complex systems and has far-reaching technological implications. While classical synchronization has a long and rich history, it has not been observed experimentally between multiple quantum limit-cycle oscillators despite a decade of theoretical investigations. We realize synchronization between two quantum van der Pol oscillators by engineering dissipation in a mixed-isotope trapped-ion quantum simulator. The synchronized state is encoded in a fixed relative phase between the oscillators that is inaccessible to individual measurements and revealed only through joint readout of both oscillators, in stark contrast to the system in the (deterministic) classical limit where synchronization can be observed via individual phase measurements. We further show that the relative phase can be precisely controlled and that the chain of two oscillators can synchronize to an external field, suggesting applications in sensing. Our results provide a promising pathway for studying more complex synchronized quantum dynamics beyond two oscillators, where a theoretical treatment becomes increasingly challenging, and it remains to be understood whether genuinely quantum features persist in such cases.

Liu, Jiarui↗

DOE OSTI2023

Forced Power Systems Oscillations Due to Cyberattacks: Threats, Detection and Partial Mitigation

Forced oscillations in power systems can be caused by misconfigured controllers at generator stations. They can also be caused by cyberattacks against the exciters or governors. This paper explores the effects of forced oscillations from cyberattacks on generator excitation and governor systems and the effectiveness of a novel control system for a static var compensator in mitigating those oscillations to enhance transmission system resilience. A brief overview of oscillations, especially forced oscillations, within power systems is presented, along with an overview of cyberattacks on power systems. This paper also examines and implements FACTS devices to partially mitigate the forced oscillations created by cyberattacks by reducing the magnitude of the oscillations caused by the attack. The proposed approach is more effective against attacks targeting exciters.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Design of Hopfield Networks Based on Superconducting Coupled Oscillators

The global energy shortage has driven the development of many energy-efficient computational platforms beyond Moore's law, among which brain-inspired neuromorphic computing is one of the promising solutions. Associative memory and pattern recognition are important computations solved by brain-inspired Hopfield networks. Classical Hopfield networks store memories via fixed point attractors of their dynamics. In oscillatory Hopfield networks, these attractors are replaced by periodic orbits. Here, we design an oscillatory Hopfield network based on coupled superconducting oscillators. We first employ a mathematical phase reduction approach to map networks of coupled superconducting rapid single flux quantum (RSFQ) ring oscillators to coupled Kuramoto phase-oscillator networks. We use this theory to numerically optimize the hardware's mutual inductances in order to directly match the phase-reduced superconducting oscillators to a model of phase-oscillator-based Hopfield networks. The resulting network can store multiple oscillatory phase-locked memory patterns and recover the patterns based on the initial phase conditions. As different pattern recognition tasks, or learning, require tunable connectivity strengths between the oscillatory nodes, we further employ a coupler circuit that enables tuning the coupling strength between two oscillators by applying an external flux. We demonstrate the functionality of our design through numerical simulations of a small example network with oscillators operating at 86 GHz and recognizing patterns within 10 ns. Our approach enables the learning and retrieval of dynamical memory patterns with a wide range of applications where rhythmic dynamic output is beneficial.

Cheng, Ran↗

DOE OSTI2024

Latest Three Flavor Neutrino Oscillation Results from the NOvA Experiment.

NOvA, is a two-detector, long-baseline neutrino oscillation experiment located at Fermilab, Batavia, IL, USA. It is designed primarily to constrain neutrino oscillation parameters such as the atmospheric mass squared splitting, $\Delta m^2_{32}$, the mixing angle, $\theta_{23}$, neutrino mass hierachy, and the CP-violating phase, $\delta_{CP}$, using $\nu_\mu \ (\bar{\nu}_\mu)$ disappearance and $\nu_e \ (\bar{\nu}_e)$ appearance data. NOvA receives a high purity instense beam of neutrinos and anti-neutrinos from Fermilab's Neutrinos at Main Injector (NuMI) beamline. The NOvA near detector (ND) observes un-oscillated $\nu_\mu \ (\bar{\nu}_\mu)$ and beam $\nu_e \ (\bar{\nu}_e)$ events, while the far detector (FD), which is situated 810 km away from the near detector, records un-oscillated $\nu_\mu \ (\bar{\nu}_\mu)$ and oscillated $\nu_e \ (\bar{\nu}_e)$ events. The best fit values of the oscillation parameters are extracted by performing a joint fit of the far detector predicted events to data from $\nu_\mu \to \nu_\mu$, $\bar{\nu}_\mu \to \bar{\nu}_\mu$, $\nu_\mu \to \nu_e$, and $\bar{\nu}_\mu \to \bar{\nu}_e$ oscillation channels. We present latest joint fit results from NOvA based on a neutrino-beam exposure of $27.24 \times 10^{20}$ POT and an anti-neutrino beam exposure of $12.55\times 10^{20}$ POT and improved simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗