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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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Universal Anomalous Diffusion of Quantized Vortices in Ultraquantum Turbulence

In classical viscous fluids, turbulent eddies are known to be responsible for the rapid spreading of embedded particles. However, in inviscid quantum fluids where the turbulence is induced by a chaotic tangle of quantized vortices, dispersion of the particles can be achieved via a nonclassical mechanism, i.e., their binding to the evolving vortices. However, knowledge on how the vortices diffuse and spread in quantum-fluid turbulence is very limited, especially for the so-called ultraquantum turbulence (UQT) generated by a random tangle of vortices. Here we report a systematic numerical study of the apparent diffusion of vortices in UQT in superfluid helium-4 using the full Biot-Savart simulation. We reveal that the vortices in the superfluid exhibit a universal anomalous diffusion (superdiffusion) at small times, which transits to normal diffusion at large times. This behavior is found to be the result of a generic scaling property of the vortex velocity. Our simulation at finite temperatures also nicely reproduces recent experimental observations. Lastly, the knowledge obtained from this study may form the base for understanding turbulent transport and universal vortex dynamics in various quantum fluids.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Numerical study on aerosol sampling in a nuclear facility duct with a 90-degree elbow

Due to the challenging design requirements, elbows are often unavoidable in duct configuration, and these 90-degree bends introduce swirl, velocity variations, recirculation, and secondary flow. These disturbances make it difficult for nuclear facilities to meet particle sampling standards. A series of numerical analyses are conducted to track aerosols in a nuclear facility duct having a 90-degree elbow with the assistance of computational fluid dynamics (CFD). A turbulence model, a continuity, and a momentum, a discrete phase model, and species transport equations are solved simultaneously to track aerosols in the duct. The effect of turbulence models, turbulent dispersion models, droplet drag model, aerosol amount, aerosol spray configuration, guide vanes, and mixers are investigated. Simulation results are analyzed per relevant testing codes such as DOE-HDBK-1169, ASME AG1, ISO 14644-3, ACGIH, and ANSI/HPS N13.1.

Han, Kai [Savannah River Nuclear Solutions (SRNS),↗
DOE OSTI2021

Physics-Informed Machine Learning Models for Predicting the Progress of Reactive-Mixing

This paper presents a physics-informed machine learning (ML) framework to construct reduced-order models (ROMs) for reactive-transport quantities of interest (QoIs) based on high-fidelity numerical simu-lations. QoIs include species decay, product yield, and degree of mixing. The ROMs for QoIs are applied to quantify and understand how the chemical species evolve over time. First, high-resolution datasets for constructing ROMs are generated by solving anisotropic reaction-di?usion equations using a non-negative finite element formulation for di?erent input parameters. The reactive-mixing model input parameters are: time-scale associated with flipping of velocity, spatial-scale controlling small/large vortex structures of velocity, perturbation parameter of the vortex-based velocity, anisotropic dispersion strength/contrast, and molecular diffusion. Second, random forests, F-test, and mutual information criterion are used to evaluate the importance of model inputs/features with respect to QoIs. We observed that anisotropic dispersion strength/contrast is the most important feature and time-scale associated with flipping of velocity is the least important feature. Third, Support Vector Machines (SVM) and Support Vector Regression (SVR) are used to construct ROMs based on the model inputs. The constructed SVR-ROMs are then used to predict scaling of QoIs. We also present estimates and inequalities on the QoIs, which inform that the species decay, mix, and produce in an exponential fashion. These inequalities also inform that a radial basis function is the most suitable kernel for the SVM/SVR models for QoIs. It is observed that R2-score for SVR-ROMs on unseen data is greater than 0.9, implying that the SVR-ROMs are able to predict the reaction-diffusion system state reasonably well. Finally, in terms of the computational cost, the proposed SVM-ROMs are O(107) times faster than running a high-fidelity finite element simulation for evaluating QoIs. This makes the proposed ML-based ROMs attractive for reactive-transport sensing and real-time monitoring applications as they are significantly faster yet reasonably accurate.

Mudunuru, Maruti K.↗
DOE OSTI2022

A finite micro-rotation material point method for micropolar solid and fluid dynamics with three-dimensional evolving contacts and free surfaces

This paper introduces an explicit material point method designed specifically for simulating the micropolar continuum dynamics in the finite deformation and finite microrotation regime. The material point method enables us to simulate large deformation problems while circumventing the potential mesh distortion without remeshing. To eliminate rotational motion damping and loss of angular momentum during the projection, we introduce the mapping for microinertia and angular momentum between particles and grids through the affine particle-in-cell approach. The microrotation and the curvature at each particle are updated through zero-order forward integration of the microgyration and its spatial gradient. We show that the microinertia and the angular momentum are conserved during the projections between particles and grids in our formulation. We verify the formulation and implementation by comparing with the analytical dispersion relation of micropolar waves under the small strain and small microrotation, as well as the analytical soliton solution for solids undergoing large deformation and large microrotation. Additionally we also demonstrate the capacity of the proposed computational framework to handle a wide spectrum of simulations that exhibit size effects in the geometrical nonlinear regime through three representative numerical examples, i.e., a cantilever beam torsion problem, a fragment-impact penetration problem, and a micropolar fluid discharging problem.

42 ENGINEERING↗
DOE OSTI2021

Droplet and Particle Methods to Investigate Turbulent Particle Laden Jets

The SARS-CoV-2 pandemic has heightened the interest in particle-laden turbulent jets generated by breathing, talking, coughing and sneezing, and how these can contribute to disease transmission. We present quantitative measurement methods for such flows, while exploring and offering improvements for common shortcomings. We generate jets consisting of either liquid droplets or solid particles in an isothermal, quiescent and electrically isopotential experimental chamber that was constructed to control the effects of ambient forcing on jet behavior. For liquid droplets, we find promise in surface deposition analysis based on fluorescent tracer use. For particles, we explore the performance of commercially available adhesive sampling strips and develop conductive grounded carbon tape based sampling strips. We explore ways in which the smallest of thermal gradients or electrostatic charge issues can affect particle dispersion, and suggest practical methods to address these issues. The developed methods are applied to study the simultaneous deposition of (Formula presented.) 25, 50 and 200 μm solid particles from a particle laden turbulent jet with a mean velocity of 33.2 m/s. The deposition location as a function of particle size was compared to results from a simple numerical RANS model, and illustrates ways in which imprecise initial or boundary conditions can lead to a notable deviation from experimental results. The differences in deposition pattern seen in experimental and numerical results despite a carefully controlled environment and characterized particle ejection indicate the need for a more stringent numerical model validation, especially when studying fate and transport of mid-range (neither purely aerosol or ballistic) sized particles.

42 ENGINEERING↗
DOE OSTI2023

Investigations of nonlinear polarization transfer between obliquely intersecting beams

Electromagnetic waves propagating through plasma can interact nonlinearly through a variety of different mechanisms. The excitation of a plasma beat wave (ions or electrons) can create a refractive index modulation that changes the dispersion of the interacting beams. Alternatively, high-intensity beams can enter the regime where relativistic nonlinearities influence the propagation dynamics. In recent studies [ Opt. Express 29 , 1162 ( 2021 ) OPEXFF 1094-4087 10.1364/OE.413064 ], it was proposed that two beams propagating along the same axis can exchange their polarization state due to nonlinear interaction. Here we present a numerical analysis of two laser beams intersecting in a nonlinear medium at varying angles. Polarization transfer is observed as predicted by analytical theory for a range of angles. For small angles, it is found that filamentation of the interacting beams becomes important. Analytical estimates of the filamentation threshold are presented, and good agreement is found with the simulation data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Numerical and Analytical Modeling of Flow Partitioning in Partially Saturated Fracture Networks

Infiltration processes in fractured-porous media remain a crucial, yet not very well understood component of recharge and vulnerability assessment. Under partially-saturated conditions flows in fractures, percolating fracture networks, and fault zones contribute to the fastest spectrum of infiltration velocities via preferential pathways. Specifically, the partitioning dynamics at fracture intersections determine the magnitude of flow fragmentation into vertical and horizontal components and hence the bulk flow velocity and dispersion of fracture networks. In this work, we derive an approximate analytical solution for the partitioning process and validate it using smoothed particle hydrodynamics simulations. The developed transfer function is conceptually based on simulation results and laboratory experiments carried out in previous works. It allows to efficiently simulate flow through fracture networks with simple cubic structure and arbitrary number of fractures and aperture sizes via linear response theory and convolution of a given input signal. We derive a non-dimensional bulk flow velocity ($\widetilde{v}$) and dispersion coefficient ($\widetilde{D}$) to characterize fracture networks in terms of dimensionless horizontal and vertical time scales $\tau_m$ and $\tau_0$. The dispersion coefficient is shown to strongly depend on the horizontal time scale and converges towards a constant value of $0.08$ within reasonable fluid and geometrical parameter ranges, while the non-dimensional velocity exhibits a characteristic $\widetilde{v} \sim \tau_m^{-1/2}$ scaling. Given that hydraulic information is often only available at limited places within (fractured-porous) aquifer system, such as boreholes or springs, our study intends to provide a rudimentary analytical concept to potentially reconstruct internal fracture network geometries from external boundary information, e.g., the dispersive properties of discharge (groundwater level fluctuations).

42 ENGINEERING↗
DOE OSTI2024

Evaluation of the Radioactive Material Release in the Harborview Research and Training Building and Implications for Emergency Response

On May 2, 2019, during the 137 Cs source recovery operation, a source capsule in a research irradiator containing approximately 77.1 TBq was breached. Based on a geometric reconstruction analysis of the damage to the capsule, approximately 46.3 GBq (0.04%) was impacted by the chop saw (grinder) inside a Mobile Hot Cell (MHC) on the loading dock at the University of Washington Harborview Research and Training (HRT) Building. A very small fraction of the material impacted, less than 1%) was released from the Mobile Hot Cell and then to the rest of the HRT Building. The objectives of this project were to assess the accidental release of 137 CsCl and its implications related to emergency response methods and the ramifications of 137 CsCl transport. The phenomenology of this event was also compared with past alkali halide dispersal events. The vast number of measurements and samples collected by the remediation contractors, the Department of Energy's Nuclear Emergency Support Team, and the small number of retrospective samples collected by the authors informed the analysis. The techniques included (1) autoradiography and electron microscopy of samples collected from the HRT Building and the irradiator, (2) 3D visualization of deposition on surfaces and within the ventilation system, and (3) a study of the damage to the source capsule to evaluate the Cs particle size and particle composition due to the grinding accident. Subsequently, the cesium contaminant transport through the numerous pathways in the building was reconstructed to assess the deposition on surfaces as a function of particle size. The implications for emergency response are relevant to data quality and management. A Data Quality Objective (DQO) guides data collection methods so that they have appropriate accuracy and precision for the intended application. Recommendations were made with respect to the sample collection protocols and sample archival.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2021

Gravitational wave propagation beyond general relativity: waveform distortions and echoes

We study the cosmological propagation of gravitational waves (GWs) beyond general relativity (GR) across homogeneous and isotropic backgrounds. We consider scenarios in which GWs interact with an additional tensor field and use a parametrized phenomenological approach that generically describes their coupled equations of motion. We analyze four distinct classes of derivative and non-derivative interactions: mass, friction, velocity, and chiral. We apply the WKB formalism to account for the cosmological evolution and obtain analytical solutions to these equations. We corroborate these results by analyzing numerically the propagation of a toy GW signal. We then proceed to use the analytical results to study the modified propagation of realistic GWs from merging compact binaries, assuming that the GW signal emitted is the same as in GR. We generically find that tensor interactions lead to copies of the originally emitted GW signal, each one with its own possibly modified dispersion relation. These copies can travel coherently and interfere with each other leading to a scrambled GW signal, or propagate decoherently and lead to echoes arriving at different times at the observer that could be misidentified as independent GW events. Depending on the type of tensor interaction, the detected GW signal may exhibit amplitude and phase distortions with respect to a GW waveform in GR, as well as birefringence effects. Furthermore, we discuss observational probes of these tensor interactions with both individual GW events, as well as population studies for both ground- and space-based detectors.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Closures for multicomponent reacting flows based on dispersion analysis

This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and diffusion. Expanding upon analysis originally developed for non-reactive transport in the context of Taylor dispersion of scalars, this work extends the modified gradient diffusion model explicated by Peters [N. Peters, Turbulent Combustion, Cambridge Monographs on Mechanics (Cambridge University Press, Cambridge, 2000)] and based on work by Corrsin [S. Corrsin, The reactant concentration spectrum in turbulent mixing with a first-order reaction, J. Fluid Mech. 11, 407 (1961)] beyond single-component transport phenomena and involving nonlinear reactions. The presented model forms, from this weakly nonlinear extension of the original dispersion theory, lead to an analytic expression for the eddy diffusivity matrix that explicitly captures the influence of the reaction kinetics on the closure operators. Furthermore, we demonstrate that the derived model form directly translates between flow topologies through a priori and a posteriori testing of a binary species system subject to homogeneous isotropic turbulence. Using two- and three-dimensional direct numerical simulations involving laminar and turbulent flows, it is shown that this framework improves prediction of mean quantities compared to previous results. Lastly, the presented model form, collapses to the earlier gradient diffusion and its modified version derived by Corrsin in the limits of nonreactive species and linear reactions, respectively.

42 ENGINEERING↗
DOE OSTI2022

Transitions in the morphology and critical stresses of gliding dislocations in multiprincipal element alloys

Refractory multiprincipal element alloys (MPEAs) are promising material candidates for high-temperature, high-strength applications. However, their deformation mechanisms, particularly at the dislocation scale, are unusual compared to those of conventional alloys, making it challenging to understand the origin of their high strength. Here, using an atomistically informed phase-field dislocation dynamics model, we study transitions in the morphology and critical stresses of long gliding screw dislocations over extended distances in a refractory MPEA. The model MPEA crystal accounts for the atomic-scale fluctuations in chemical composition across the glide planes via spatially correlated lattice energies and for the differences in glide resistances between screw and edge dislocations of unit length. Here, we show that the dislocation moves in a stop-start motion, alternating between wavy morphology in free flight and nearly recovered straight screw orientation in full arrest. The periods of wavy glide are due to variable kink-pair formation and migration rates along the length, where portions with higher rates glide more quickly. The critical stress to initiate motion corresponds to the stress required to form and migrate a kink pair at the weakest region along the length of the dislocation. Heterogeneity in lattice energy leads to variability in the local stress-strain response and to a strain hardening-like response, in which the critical stress to reactivate glide increases with glide distance. Statistical assessment of hundreds of realizations of dislocations indicates that the amount of hardening directly scales with the dispersion in underlying lattice energy.

3-dimensional systems↗
DOE OSTI2021

Spectral properties and enhanced superconductivity in renormalized Migdal-Eliashberg theory

Migdal-Eliashberg theory describes the properties of the normal and superconducting states of electron-phonon-mediated superconductors based on a perturbative treatment of the electron-phonon interactions. It is necessary to include both electron and phonon self-energies self-consistently in Migdal-Eliashberg theory in order to match numerically exact results from determinantal quantum Monte Carlo in the adiabatic limit. Here in this work we provide a method to obtain the real-axis solutions of the Migdal-Eliashberg equations with electron and phonon self-energies calculated self-consistently. Our method avoids the typical challenge of computing cumbersome singular integrals on the real axis and is numerically stable and exhibits fast convergence. Analyzing the resulting real-frequency spectra and self-energies of the two-dimensional Holstein model, we find that self-consistently including the lowest-order correction to the phonon self-energy significantly affects the solution of the Migdal-Eliashberg equations. The calculation captures the broadness of the spectral function, renormalization of the phonon dispersion, enhanced effective electron-phonon coupling strength, minimal increase in the electron effective mass, and the enhancement of superconductivity which manifests as a superconducting ground state despite strong competition with charge-density-wave order. We discuss surprising differences in two common definitions of the electron-phonon coupling strength derived from the electron mass and the density of states, quantities which are accessible through experiments such as angle-resolved photoemission spectroscopy and electron tunneling. An approximate upper bound on 2Δ/T c for conventional superconductors mediated by retarded electron-phonon interactions is proposed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Fault-Tolerant Operation of Bosonic Qubits with Discrete-Variable Ancillae

Fault-tolerant quantum computation with bosonic qubits often necessitates the use of noisy discrete-variable ancillae. In this work, we establish a comprehensive and practical fault-tolerance framework for such a hybrid system and synthesize it with fault-tolerant protocols by combining bosonic quantum error correction (QEC) and advanced quantum control techniques. We introduce essential building blocks of error-corrected gadgets by leveraging ancilla-assisted bosonic operations using a generalized variant of path-independent quantum control. Using these building blocks, we construct a universal set of error-corrected gadgets that tolerate a single-photon loss and an arbitrary ancilla fault for four-legged cat qubits. Notably, our construction requires only dispersive coupling between bosonic modes and ancillae, as well as beam-splitter coupling between bosonic modes, both of which have been experimentally demonstrated with strong strengths and high accuracy. Moreover, each error-corrected bosonic qubit is comprised of only a single bosonic mode and a three-level ancilla, featuring the hardware efficiency of bosonic QEC in the full fault-tolerant setting. We numerically demonstrate the feasibility of our schemes using current experimental parameters in the circuit-QED platform. Finally, we present a hardware-efficient architecture for fault-tolerant quantum computing by concatenating the four-legged cat qubits with an outer qubit code utilizing only beam-splitter couplings. Our estimates suggest that the overall noise threshold can be reached using existing hardware. These developed fault-tolerant schemes extend beyond their applicability to four-legged cat qubits and can be adapted for other rotation-symmetrical codes, offering a promising avenue toward scalable and robust quantum computation with bosonic qubits. Published by the American Physical Society 2024

Physics↗
DOE OSTI2023

Minimal one-dimensional model of bad metal behavior from fast particle-hole scattering

A strongly interacting plasma of linearly dispersing electron and hole excitations in two spatial dimensions (2D), also known as a Dirac fluid, can be captured by relativistic hydrodynamics and shares many universal features with other quantum critical systems. Here, we propose a one-dimensional (1D) model to capture key aspects of the 2D Dirac fluid while including lattice effects and being amenable to nonperturbative computation. When interactions are added to the Dirac-like 1D dispersion without opening a gap, we show that this kind of irrelevant interaction is able to preserve Fermi-liquid-like quasiparticle features while relaxing a zero-momentum charge current via collisions between particle-hole excitations, leading to resistivity that is linear in temperature via a mechanism previously discussed for large-diameter metallic carbon nanotubes. We further provide a microscopic lattice model and obtain numerical results via density-matrix renormalization group simulations, which support the above physical picture. The limits on such fast relaxation at strong coupling are of considerable interest because of the ubiquity of bad metals in experiments.

1-dimensional systems↗
DOE OSTI2022

Toward Accurate Modeling of Galaxy Clustering on Small Scales: Constraining the Galaxy-halo Connection with Optimal Statistics

Applying halo models to analyze the small-scale clustering of galaxies is a proven method for characterizing the connection between galaxies and their host halos. Such works are often plagued by systematic errors or limited to clustering statistics that can be predicted analytically. In this work, we employ a numerical mock-based modeling procedure to examine the clustering of Sloan Digital Sky Survey DR7 galaxies. We apply a standard halo occupation distribution (HOD) model to dark matter only simulations with a ΛCDM cosmology. To constrain the theoreStical models, we utilize a combination of galaxy number density and selected scales of the projected correlation function, redshift-space correlation function, group multiplicity function, average group velocity dispersion, mark correlation function, and counts-in-cells statistics. We design an algorithm to choose an optimal combination of measurements that yields tight and accurate constraints on our model parameters. Compared to previous work using fewer clustering statistics, we find a significant improvement in the constraints on all parameters of our halo model for two different luminosity-threshold galaxy samples. Most interestingly, we obtain unprecedented high-precision constraints on the scatter in the relationship between galaxy luminosity and halo mass. However, our best-fit model results in significant tension (>4σ) for both samples, indicating the need to add second-order features to the standard HOD model. To guarantee the robustness of these results, we perform an extensive analysis of the systematic and statistical errors in our modeling procedure, including a first of its kind study of the sensitivity of our constraints to changes in the halo mass function due to baryonic physics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Nature of polariton transport in a Fabry-Perot cavity

Fabry-Perot microcavities can strongly enhance interactions between light and molecules, leading to the formation of hybrid light-matter states known as polaritons. Polaritons possess much smaller effective masses and much larger group velocities when the molecules are resonant with cavity modes that have finite (nonzero) in-plane wave vectors, giving rise to the possibilities of long-range and ultrafast ballistic transport. In this paper, we present the results of numerical simulations of the ultrafast ballistic transport phenomenon in real space and time during and after initialization with a short, spatially localized pulse. Here, we address this problem with two approaches: the standard transfer-matrix method (TMM) for planar structures and a second simulation based on the numerical solution of the Maxwell-Bloch equations that can be used for general configurations (complex metasurfaces, for instance) and excitation modes. The agreement between the TMM and the full numerical calculation with the Maxwell-Bloch equations when applied to multilayer planar configurations provides proof of the validity of both approaches for the present analyses. Overall, we find that the transport of the molecular excitons inside the cavity synchronize with the evolution of the enhanced electromagnetic field inside the cavity. Moreover, the synchronized transport rate is in good agreement with the group velocities predicted from a calculated dispersion relation across a wide range of frequencies. Finally, we relate the group velocity to the Hopfield coefficient obtained from quantum modeling and suggest that the dependence of light-matter coupling on the in-plane wave vector can be an important but overlooked factor for understanding the transport behavior of polaritons. These simulations provide an intuitive tool for understanding the collective motion of light and excitons and helps us to better understand how experimental observations of polaritons should be interpreted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Spin dynamics and exchange interaction in orthoferrite TbFeO 3 with non-Kramers rare-earth ion

The low-temperature spin dynamics of the orthorhombic TbFeO 3 perovskite has been studied. It has been found that the inelastic neutron scattering (INS) spectrum of the investigated compound contains two modes corresponding to different sublattices. It is shown that the iron subsystem orders antiferromagnetically at T N =632 K and exhibits the high-energy magnon dispersion. The magnetic dynamics of this subsystem has been described within the linear spin wave theory and the in-plane and out-of-plane exchange anisotropy has been demonstrated. The approach proposed previously to describe the magnon dispersion in the TmFeO 3 compound has been used. Three levels of the nondispersive crystal electric field corresponding to Tb 3+ ions have been found in the energy region below 40 meV at about 17, 26, and 35 meV. The behavior of the magnetic correlation length of the terbium subsystem has been determined by studying the diffuse scattering at different temperatures. The evolution of this subsystem has been numerically described within the point charge model. In conclusion, it is shown that the numerical data agree satisfactorily with the experiment and with the general concept of the single-ion approximation applied to the rare-earth subsystem of orthorhombic perovskites.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Jamming Detection for Low-Resolution SC-FDE Systems: A Machine Learning Approach

Jammers interfere with communication between base stations (BSs) and legitimate users, leading to degradation of wireless system performance. Our study focuses on jamming detection for wideband single-carrier frequency domain equalization (SC-FDE) systems with low-resolution analog-to digital converters (ADCs). In such systems, jamming detection is challenging because traditional analytical approaches cannot be directly applied due to the delay dispersion in wideband channels and the non-linearity induced by low-resolution ADCs. We propose a machine learning (ML)-based jamming detection method that directly uses the quantized receive signals. Significantly, our ML-based detector can be integrated into existing standard frameworks, such as unique word (UW)-based SC-FDE systems, as it uses existing pilots without requiring additional pilots for jamming detection. Through numerical simulations, we show that two or more bits provide satisfactory performance compared to unquantized scenarios. Additionally, we demonstrate that using more and well-separated pilot symbols improves performance.

99 GENERAL AND MISCELLANEOUS↗