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Material Characterization For Industrial Processes Of Thin Titanium Nanotube Films, Nathaniel Jobson, Jacob Walther, Justin Rink, Wil Pinkerton Apr 2024

Material Characterization For Industrial Processes Of Thin Titanium Nanotube Films, Nathaniel Jobson, Jacob Walther, Justin Rink, Wil Pinkerton

23rd Annual A. Paul and Carol C. Schaap Celebration of Undergraduate Research and Creative Activity (2024)

Material characterization is an important step in the experimental processes. This step ensures that the samples' processing yields the intended results. This work outlines the process taken to analyze and characterize a set of industrial thin films. Our characterization starts with an elemental baseline from scanning electron microscopy (SEM). The composition is verified by SimNRA (Simulation Nuclear Reaction Analysis) calculations fitting Rutherford Backscattering (RBS) data collected from a silicon surface barrier (particle) detector.


Turbulence And Zonal-Flow Impact In The Madison Symmetric Torus In Quasi-Single Helicity, Nicholas J. Kaipainen, Y. L. De Jong, L. Helder, M. J. Pueschel, J. S. Sarff, P. W. Terry, P. D. Vanmeter Apr 2024

Turbulence And Zonal-Flow Impact In The Madison Symmetric Torus In Quasi-Single Helicity, Nicholas J. Kaipainen, Y. L. De Jong, L. Helder, M. J. Pueschel, J. S. Sarff, P. W. Terry, P. D. Vanmeter

23rd Annual A. Paul and Carol C. Schaap Celebration of Undergraduate Research and Creative Activity (2024)

Reversed-Field Pinches (RFPs) operating in the Quasi-Single-Helicity (QSH) magnetic geometry exhibit significant improvements in confinement time as compared to standard discharges due to the efficient saturation of large-scale tearing modes. This modification to the magnetic geometry and profiles introduces new instabilities which drive transport. This work focuses on diagnosing the microinstabilities and microturbulence in a non-reversed Madison Symmetric Torus QSH experiment. Local gyrokinetic simulations are conducted with the GENE code to identify the dominant instabilities as ion-temperature-gradient (ITG) and density-gradient-driven trapped-electron-mode (TEM) at core and edge radial locations, respectively. It has been previously observed in the RFP (Williams PoP 2017) …


Β-Decay Strength Function Of 53ni And 52co, Gabe A. Balk, A. Spyrou, M. K. Smith, W. Von Seeger Apr 2024

Β-Decay Strength Function Of 53ni And 52co, Gabe A. Balk, A. Spyrou, M. K. Smith, W. Von Seeger

23rd Annual A. Paul and Carol C. Schaap Celebration of Undergraduate Research and Creative Activity (2024)

The p process is believed to be responsible for the formation of heavy proton-rich nuclei in the universe. This work deals with the decay of two nuclei that are part of the p process, 53Ni and 52Co. β+ decays for each isotope were recorded with the Summing NaI(Tl) detector at the National Superconducting Cyclotron Laboratory. A preliminary β-decay Intensity Function was derived with Total Absorption Spectroscopy. Total energy spectra, β-particle spectra, individual γ-energy spectra, and multiplicity spectra for the decay to levels in the child nucleus were modeled with GEANT4 based on information from the National Nuclear Data …


Investigation Of Convection Cells Via Truncated Eigenmode Decomposition, Gillian Donley, A. E. Fraser Apr 2024

Investigation Of Convection Cells Via Truncated Eigenmode Decomposition, Gillian Donley, A. E. Fraser

23rd Annual A. Paul and Carol C. Schaap Celebration of Undergraduate Research and Creative Activity (2024)

Convection cells are found in a variety of contexts throughout physics, including plasmas within the stellar interior and in neutral fluids such as planetary atmospheres. Rayleigh Benard Convection (RBC) is the most well studied model for this behavior, describing convection in fluids that are heated from below and cooled from above, resulting in a temperature gradient which can drive instabilities. Under the right conditions, this instability develops and drives convective heat transport, which is still actively researched in fluid and plasma dynamics today. We study the neutral fluid configuration of this system using a novel modeling approach that approximates the …


Β-Decay Strength Function Of 99,100 Y, Nathaniel Jobson, A. Spyrou Apr 2024

Β-Decay Strength Function Of 99,100 Y, Nathaniel Jobson, A. Spyrou

23rd Annual A. Paul and Carol C. Schaap Celebration of Undergraduate Research and Creative Activity (2024)

The rapid neutron capture process (r process) is responsible for the formation of numerous nuclei in the universe. To obtain better models for heavier nuclei that are part of the r process, the decay paths of 99,100Y were analyzed. This work was done using the Summing NaI(Tl) detector at the National Superconducting Cyclotron Laboratory. The Iβ(E) and the Beta Gamow-Teller function (BGT) were extracted from the measured Total Absorption Spectroscopy (TAS), Sum of Segments (SEG), and Multiplicity spectrum. The Iβ(E) and the Beta Gamow-Teller function (BGT) were extracted from the measured spectra and then compared to the Quasi Random Phase …


Quantifying The Effect Of Air On Uncertainty In The Particle Accelerator, Megan Haeussler, Evelyn Martin, Zachary Doctor Apr 2024

Quantifying The Effect Of Air On Uncertainty In The Particle Accelerator, Megan Haeussler, Evelyn Martin, Zachary Doctor

23rd Annual A. Paul and Carol C. Schaap Celebration of Undergraduate Research and Creative Activity (2024)

In preparation to measure environmental PFAS contamination, we are quantifying measurement uncertainties of liquid Sodium-Fluoride (NaF) standards undergoing particle induced gamma emission (PIGE). These standards are measured in the atmosphere outside of the vacuum environment of the particle accelerator at Hope College. One source of uncertainty is the dimensions of the experimental setup. If the target is even one millimeter farther away from the exit window than anticipated, the beam will lose energy as it travels through the air and will not be able to penetrate as far into the target as expected. We aim to quantify the uncertainty caused …


Development Of A Consistent Proton Induced Gamma Emission Liquid 19f Standard, Jordan Craft, Ryan Mccreedy, Naomi Whitfield, Loic Rutabana Apr 2024

Development Of A Consistent Proton Induced Gamma Emission Liquid 19f Standard, Jordan Craft, Ryan Mccreedy, Naomi Whitfield, Loic Rutabana

23rd Annual A. Paul and Carol C. Schaap Celebration of Undergraduate Research and Creative Activity (2024)

We developed a new technique to quantify PFAS (Fluorine) contamination in water using Hope College’s particle accelerator. To do this, we created an ~2000 PPM NaF in water standard and carefully controlled the experimental configuration. We are hoping that careful control of the experimental conditions will yield a consistent 19F gamma-ray count per Coulombs from Proton Induced Gamma-ray Emission (PIGE). 3.4MeV protons have enough energy to exit the particle accelerator, travel 27 mm in air, and penetrate into the liquid standard. As protons lose energy in the liquid, nuclear reactions such as (p, p’gamma) with the 19F and 23Na nuclei …


Machine Learning Techniques For Intermediate Mass Gap Lepton Partner Searches At The Large Hadron Collider, Bhaskar Dutta, Tathagata Ghosh, Alyssa Horne, Jason Kumar, Sean Palmer, Pearl Sandick, Marcus Snedeker, Patrick Stengel, Joel W. Walker Apr 2024

Machine Learning Techniques For Intermediate Mass Gap Lepton Partner Searches At The Large Hadron Collider, Bhaskar Dutta, Tathagata Ghosh, Alyssa Horne, Jason Kumar, Sean Palmer, Pearl Sandick, Marcus Snedeker, Patrick Stengel, Joel W. Walker

Michigan Tech Publications

We consider machine learning techniques associated with the application of a boosted decision tree (BDT) to searches at the Large Hadron Collider (LHC) for pair-produced lepton partners which decay to leptons and invisible particles. This scenario can arise in the minimal supersymmetric Standard Model (MSSM), but can be realized in many other extensions of the Standard Model (SM). We focus on the case of intermediate mass splitting (∼30 GeV) between the dark matter (DM) and the scalar. For these mass splittings, the LHC has made little improvement over LEP due to large electroweak backgrounds. We find that the use of …


Simulating Ice Nuclei Under Atmospheric Electric Fields, Joseph Cooney Apr 2024

Simulating Ice Nuclei Under Atmospheric Electric Fields, Joseph Cooney

Student Research Symposium

Orographic clouds generally form over mountains when valleys are sunny. The unstable atmosphere can trigger clouds over the mountains, which can be convective. When this happens, the cloud particles (water droplets and ice particles) become charged, ultimately creating ice crystals. In this study, we want to evaluate the impact of electricity on the formation of ice crystals and used a simulation to do so.


Teaching A Computer To Do Mechanics, Andrew Watson Apr 2024

Teaching A Computer To Do Mechanics, Andrew Watson

Student Research Symposium

Classical Mechanics

- Used for determining motion of objects

- Three Main Formulations of Classical Mechanics

  • Newtonian Mechanics: Revolves around Newton’s 2nd Law (F = ma)
  • Lagrangian Mechanics: Revolves around the Lagrangian
  • Hamiltonian Mechanics: Revolves around the Hamiltonian

- Hamiltonian Mechanics provides the most powerful view of mechanics – but it’s complicated!

  • My goal is to get the computer to do Hamiltonian Mechanics.


Amorphous Transparent Oxide P-Type Semiconductors, Joshua Santy Apr 2024

Amorphous Transparent Oxide P-Type Semiconductors, Joshua Santy

Undergraduate Research Conference at Missouri S&T

For decades, n-type transparent conducting oxides (TCOs) have been extensively studied and applied in various energy and optoelectronic devices. However, the search for high-performance p-type TCOs, crucial for transparent p-n junctions and next-generation microelectronics - remains uncertain. The most studied p-type TCOs (e.g ., Cu2O-based delafossite family) exhibit the carrier mobilities (<1 cm2Ns) that are much smaller than those in typical n-type TCOs (10-100 cm2Ns). In contrast to the Cu-based layered materials with a relatively flat Cu d10 valence band (resulting in the hole effective mass of 2.5me), Sn2+ in SnO has s2 electronic configuration giving rise to a significantly more dispersed valence band (the hole effective mass is 0.5me) and, hence, to higher hole mobility. Currently, the practical use of SnO is limited due to (i) stability issues of SnO associated with tin preference for valence 4 (as in SnO2, a well-known n-type TCO); (ii) small band gap ~0.7 eV; and (iii) anisotropic hole effective mass in the crystalline phase. Further search for p-type TCOs should involve amorphous phases of SnO-based multi-cation materials where metal composition helps stabilize Sn2+ and open the band gap, whereas the disordered structure is expected to result in uniform isotropic electronic properties and low scattering due to absence of grain boundaries.


Enhancing Galaxy Surveys With Machine Learning, Steven Karst Apr 2024

Enhancing Galaxy Surveys With Machine Learning, Steven Karst

Undergraduate Research Conference at Missouri S&T

Applications of machine learning (ML) or artificial intelligence (Al) to problems in astrophysics and cosmology have recently entered a golden era. In response, we have updated two of our recent ML/Al efforts that contribute to galaxy surveys whose main scientific target is to reveal the nature of the Comsic Acceleration or Dark Energy. We first revised our effort to infer cosmological information beyond the survey geometry using Graph Neural Networks (GNNs) to take advantage of supercomputing resources on campus. We then updated our methods for galaxy target selection in the Subaru Prime Focus Spectrograph (PFS) survey with modern reinforcement learning …


Enhancing Galaxy Surveys With Machine Learning, Steven Karst Apr 2024

Enhancing Galaxy Surveys With Machine Learning, Steven Karst

Undergraduate Research Conference at Missouri S&T

Applications of machine learning (ML) or artificial intelligence (AI) to problems in astrophysics and cosmology have recently entered a golden era. In response, we have updated two of our recent ML/ AI efforts that contribute to galaxy surveys whose main scientific target is to reveal the nature of the Cosmic Acceleration or Dark Energy. We first revised our effort to infer cosmological information beyond the survey geometry using Graph Neural Networks (GNN) to take advantage of supercomputing resources on campus. We then updated our reinforcement learning methods for galaxy target selection in the Subaru Prime Focus Spectrograph (PFS) survey with …


Visualization Of Ultracold Atomic Samples, Samuel Schrader Apr 2024

Visualization Of Ultracold Atomic Samples, Samuel Schrader

Undergraduate Research Conference at Missouri S&T

Laser cooling techniques have evolved into a powerful experimental tool to perform precision spectroscopy (for instance, atomic clocks), study fundamental few-body dynamics, and create well-controlled systems for quantum information applications. When the atoms are captured, it is critical to analyze the laser-cooled atomic samples carefully and characterize their properties, such as density, temperature, population distribution, etc., in order to perform these advanced tasks. A straightforward way to measure these properties is detecting the visible optical photons emitted from the sample with a camera. Throughout this project, I have written and developed a computer application that controls a camera and extracts …


The 2022 Hunga Tonga Volcanic Eruption's Impact On Radio Communications, Spencer Brothers Apr 2024

The 2022 Hunga Tonga Volcanic Eruption's Impact On Radio Communications, Spencer Brothers

Student Research Symposium

On January 15th 2022, the Hunga Tonga volcanic eruption, Figure 1, ejected unprecedented amounts of water into the stratosphere. The resulting plume may present temporary opportunities for long distance radio communication.


Stripe Order, Impurities, And Symmetry Breaking In A 3-Dimensional Model Of A Diluted Frustrated Magnet, James Elverson, Thomas Vojta Apr 2024

Stripe Order, Impurities, And Symmetry Breaking In A 3-Dimensional Model Of A Diluted Frustrated Magnet, James Elverson, Thomas Vojta

Undergraduate Research Conference at Missouri S&T

Many quantum materials feature low-temperature phases that break realspace symmetries in addition to spin or charge symmetries. Examples include stripe phases in cuprate superconductors, nematic phases in iron pnictides, and spin-density waves in magnetic materials. Realistic materials always contain some quenched disorder or randomness. To understand the effect of disorder on phases that break real-space symmetries, we investigate the influence of spinless impurities on a frustrated 3-dimensional J 1-J2 Ising model through Monte Carlo simulations. Spin less impurities generate random field type disorder for the spin-density wave (stripe) phase in this system. Whereas the long-range stripe order is destroyed by …


Development Of Colpitts Self Oscillator, Jasmin Billingsley Apr 2024

Development Of Colpitts Self Oscillator, Jasmin Billingsley

Undergraduate Research Conference at Missouri S&T

Topological materials can serve as promising platforms for next-generation technology. Magnetism in such systems is often a consequence of emergent quantum phenomena, and the traditional framework is insufficient to fully describe their magnetic properties. In this project, we will perform precision magnetic measurements utilizing the Colpitts self-oscillator to determine the temperature- and field-dependent AC magnetic susceptibility in the topological magnetic materials. The collective knowledge learned from this proposed research would shed light on the understanding of exotic magnetism in topological materials, potentially leading to new physics of magnetism.


Development Of Colpitts Self Oscillator For Measurement Of Magnetic And Superconducting Properties, Jasmine Billingsley Apr 2024

Development Of Colpitts Self Oscillator For Measurement Of Magnetic And Superconducting Properties, Jasmine Billingsley

Undergraduate Research Conference at Missouri S&T

Topological materials can serve as promising platforms for next-generation technology. Magnetism in such systems is often a consequence of emergent quantum phenomena, and the traditional framework is insufficient to fully describe their magnetic properties. In this project, we will perform precision magnetic measurements utilizing the Colpitts self-oscillator to determine the temperature- and field-dependent AC magnetic susceptibility in the topological magnetic materials. The collective knowledge learned from this proposed research would shed light on the understanding of exotic magnetism in topological materials, potentially leading to new physics of magnetism.


High Powered Rocket Modification, Joshua Gage Apr 2024

High Powered Rocket Modification, Joshua Gage

SACAD: Scholarly Activities

Rocketry has always been a fun challenge for me. Since not only was I able to learn something new every time I did it, but I was able to do something with my hands as well. One area that has been very challenging for me is how to put a tracker onto a rocket that has no electronics bay. And studying for the L2 Certification tests. And this poster shows my thoughts and process I did to pass my L2 Certification Flight.


Computational Modeling Of Retinal Damage Thresholds, Payton Hoffman, Eos Shapland, Alan Enriquez Apr 2024

Computational Modeling Of Retinal Damage Thresholds, Payton Hoffman, Eos Shapland, Alan Enriquez

SACAD: Scholarly Activities

The Scalable Effects Simulation Environment(SESE), is the computational Biophysics software contracted by Nanohmics we used for our research. The goal was to find the minimum energy necessary to damage the retina from 2 laser sources, a 532 nm He-Ne source, and Supercontinuum Laser(SCL) source at 400-1400nm. We needed a 10 times damage ratio for significance. Our data did not show this trend.


A Precise Measurement Of The Lifetime Of B-Mesons, Measurement Of Cp-Violation Parameters Of Bs-Mesons, The Atlas Experiment At The Lhc, And Development Of Silicon Detectors For Future Particle Physics Experiments, Easwar Anand Narayanan Apr 2024

A Precise Measurement Of The Lifetime Of B-Mesons, Measurement Of Cp-Violation Parameters Of Bs-Mesons, The Atlas Experiment At The Lhc, And Development Of Silicon Detectors For Future Particle Physics Experiments, Easwar Anand Narayanan

Physics & Astronomy ETDs

A series of connected research projects has been carried out for the purpose of seeking physics phenomena beyond the Standard Model. These consist of a precise measurement of the lifetime of a short-lived b-hadron, the Bd-meson; preparations for measurements of CP-violating parameters in Bs decays; development of triggers that select b-hadron events; development of new instruments for improved precision in detecting fundamental particles; and monitoring and mitigating the effect of radiation on the detectors, which is inescapable in their operating environment. Datasets collected by the ATLAS detector at the Large Hadron Collider (LHC) are used for …


Quantum Computation Using Large Spin Qudits, Sivaprasad Thattupurackal Omanakuttan Apr 2024

Quantum Computation Using Large Spin Qudits, Sivaprasad Thattupurackal Omanakuttan

Physics & Astronomy ETDs

This dissertation explores quantum computation using qudits encoded into large spins, emphasizing the concept of quantum co-design to harness the unique capabilities of physical platforms for enhanced quantum information processing. First, we delve into the generation of high-fidelity universal gate sets for quantum computation with qudits. Leveraging principles from quantum optimal control, Rydberg physics, and the atomic structure of alkaline-earth atoms, we propose protocols for high-fidelity universal gate sets in the ground state of 87Sr with reasonable experimental parameters. Next, we analyze schemes to encode a qubit in the large spin qudits for fault-tolerant quantum computation (FTQC). By comprehending …


Analyzing Atmospheric Gravity Waves Over Antarctica And Visualizing Machine Learning Data, Anastasia Brown Apr 2024

Analyzing Atmospheric Gravity Waves Over Antarctica And Visualizing Machine Learning Data, Anastasia Brown

Student Research Symposium

  • Gravity Waves are buoyancy waves that propagate in the atmosphere [1]
    • Mostly generated by tropospheric weather,
    • Can vertically propagate above 100 km altitude,
    • Affect the temperature structure of the atmosphere, 
    • Drive pole-to-pole circulation.


Solar Factors Influence High Frequency (Hf) Radio Propagation, Jayson Wiggins Apr 2024

Solar Factors Influence High Frequency (Hf) Radio Propagation, Jayson Wiggins

Student Research Symposium

Although it has been around for over 100 years, high frequency (HF) radio is here to stay.

HF radio is in the range from 3-30 MHz, and is used by amateur radio enthusiasts, commercial airlines, and the Department of Defense.

Communication over greater distances than other methods is possible due to skywave propagation, a process in which radio waves are reflected by the lower regions of the ionosphere. This means changes in the ionosphere have important effects on propagation.


Float Like A Butterfly, Sting Like A Bee!, Kobe D. Rome Apr 2024

Float Like A Butterfly, Sting Like A Bee!, Kobe D. Rome

SACAD: Scholarly Activities

By injecting an electron into the empty pie* molecular orbital (LUMO) of Amino Acids in gas phase, we measure the Vertical Attachment Energies (VAEs) for the formation of short-lived anion states of these species using electron transmission spectroscopy (ETS). Our ETS study, a first of its kind to measure the VAE for the simplest of proteins, Glycine-Glycine (Gly-Gly), is currently in progress. Based on our previous measurements for several Amino Acids including Glycine, we expect a common range of attachment energy (1.50 – 2.00 eV) for Gly-Gly.


All-Optical Probes Of Particle-Like Charge Migration Dynamics, Kyle A. Hamer Apr 2024

All-Optical Probes Of Particle-Like Charge Migration Dynamics, Kyle A. Hamer

LSU Doctoral Dissertations

Particle-like charge migration (CM) is the coherent, back-and-forth motion of a positively-charged electron hole along the backbone of a molecule following a sudden ionization. CM in small molecules generally occurs on an Angstrom (10-10 m) spatial scale and an attosecond (10-18 s) timescale. I use time-dependent density-functional theory (TDDFT) to simulate CM modes in organic molecules, and to explore all-optical probes of this attosecond electron dynamics using high-harmonic spectroscopy (HHS). By leveraging my results from previous studies of two-center interferences in carbon dichalcogens, in which I separated the harmonic signal into contributions from individual Kohn-Sham orbitals, I first …


Post-Modeling Adjustments And Delivered Dose Verification Of The 6fff Beam Model Commissioned For The Monaco Treatment Planning System, Grant C. Debevec Apr 2024

Post-Modeling Adjustments And Delivered Dose Verification Of The 6fff Beam Model Commissioned For The Monaco Treatment Planning System, Grant C. Debevec

LSU Master's Theses

External beam radiation therapy has been shown to be an effective treatment method for tumors and abnormalities of the spine and vertebral region. Treating the spine using a stereotactic body radiation therapy (SBRT) technique can reduce toxicity to the spinal cord. The 6 MV flattening filter free (6FFF) beam model is currently used to plan and calculate dose for SBRT treatment plans, and the treatment plans are delivered using a linear accelerator (LINAC).

The commissioned beam model represents an invariant component of a LINAC. For volumetric modulated arc therapy (VMAT) treatment plans, the multileaf collimator (MLC) positions are changing throughout …


Igniting Passion:​ A Detailed Journey Through Rocketry Course Activities, Krish M. Patel, Hannah Caycedo, Joshua Gage, Josi Maness, Kevin Park, Mufeng Shen Apr 2024

Igniting Passion:​ A Detailed Journey Through Rocketry Course Activities, Krish M. Patel, Hannah Caycedo, Joshua Gage, Josi Maness, Kevin Park, Mufeng Shen

SACAD: Scholarly Activities

This course is a semester-long adventure in rocketry, led by Dr. Paul Adams. It covers everything about building and flying rockets, starting from the basics to more advanced rocketry. Students learn how to build rockets and use equipment used I payload systems like and altimeter and a GPS. We also learned about the importance of safety involved with building and launching rockets.


A Search For Intermediate-Mass Black Holes In Compact Stellar Systems Through Optical Emissions From Tidal Disruption Events, Richard T. Pomeroy, Mark A. Norris Apr 2024

A Search For Intermediate-Mass Black Holes In Compact Stellar Systems Through Optical Emissions From Tidal Disruption Events, Richard T. Pomeroy, Mark A. Norris

Physics & Astronomy Faculty Publications

Intermediate-mass black holes (IMBH) are expected to exist in globular clusters (GCs) and compact stellar systems (CSS) in general, but none have been conclusively detected. Tidal disruption events (TDEs), where a star is tidally disrupted by the gravitational field of a black hole, have been observed to occur around the supermassive black holes (SMBH) found at the centres of galaxies, and should also arise around IMBHs, especially in the dense stellar cores of CSS's. However, to date none have been observed in such environments. Using data from the Zwicky Transient Facility (ZTF) we search for TDEs associated with CSS, but …


Constraints On Metastable Superheavy Dark Matter Coupled To Sterile Neutrinos With The Pierre Auger Observatory, A. Abdul Halim, P. Abreu, M. Aglietta, I. Allekotte, K. Almeida Cheminant, A. Almela, B. Fick, K. Nguyen, D. Nitz, Et Al. Apr 2024

Constraints On Metastable Superheavy Dark Matter Coupled To Sterile Neutrinos With The Pierre Auger Observatory, A. Abdul Halim, P. Abreu, M. Aglietta, I. Allekotte, K. Almeida Cheminant, A. Almela, B. Fick, K. Nguyen, D. Nitz, Et Al.

Michigan Tech Publications

Dark matter particles could be superheavy, provided their lifetime is much longer than the age of the Universe. Using the sensitivity of the Pierre Auger Observatory to ultrahigh energy neutrinos and photons, we constrain a specific extension of the Standard Model of particle physics that meets the lifetime requirement for a superheavy particle by coupling it to a sector of ultralight sterile neutrinos. Our results show that, for a typical dark coupling constant of 0.1, the mixing angle θm between active and sterile neutrinos must satisfy, roughly, θm≲1.5×10-6(MX/109 GeV)-2 for a mass MX of the dark-matter particle between 108 GeV …