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As we seek to understand the smallest, physical aspects of our universe, we cannot simply rely on our senses to probe the world around us as we did in the past. The smallest physical elements of our universe behave in strange, probabilistic ways and are completely invisible to the naked eye/ear/etc. So, we design clever experiments (such as scattering experiments) to probe these minute realms. Then, just as with the larger, observable world, we devise models and equations to describe what we think is happening. Due to the nature of the physical universe at the quantum scale and with the aid of symmetries such as Lorentz invariance, we can write down equations that describe the scattering, but the expressions contain functions, which we call ?form factors? and ?structure functions?, that we cannot compute from first principles. We can, however, formulate models that make predictions for these functions. By comparing our predictions with the observed data, we can gain insight into the validity of our models and thus a better physical understanding of what is happening at these minuscule scales. Studying the constituents inside of the nucleus of an atom adds another layer of difficulty if we can?t remove those components from the nucleus. This is the case with the neutron. When not bound in the nucleus with protons and other neutrons, the neutron will decay into a proton after about 15 minutes. So, we?re forced to study the neutron while it is still bound in the nucleus of an atom such as helium-3 (3He). For the last 1,000 years (rounding up), our group has developed high quality, polarized 3He targets made of an aluminosilicate glass. These targets are made in order to perform experiments at Jefferson Lab (JLab), experiments which let us determine the form factors and structure functions of the neutron by scattering polarized electrons from polarized neutrons (or rather polarized 3He). The specific experiments reported on in this thesis push the bounds of our understanding of the internal structure of the neutron. Good science is often about pushing experimental techniques to a new level. Toward that goal we study our polarized 3He targets both to advance the technology and to choose the best ones for our experiments. We do this using a process called nuclear magnetic resonance (NMR) to gauge the maximum polarization of a target and how fast the polarization decays with time. While these tests primarily provide us information that make analysis of our experimental scattering data possible, they also let us determine whether or not a target-cell is useful or even, dare I say, of spectacular quality. Our latest targets utilize a novel convection design allowing 3He to be polarized and quickly moved in front of the electron-beam, making it possible to use larger targets with higher electron-beam currents than ever before. This means more electrons scatter and we get more data. And by studying our targets in detail prior to using them in our experiments, we have found techniques to take effects which could have been detrimental to target quality and turn them to our advantage! It?s a real case of making lemonade out of lemons. We also use laser spectroscopy to study the absorption lines of alkali-metals in the target (potassium and rubidium, specifically). We add these alkali-metals to our target to facilitate polarizing the 3He. We can use the measurement of these pressure broadened absorption lines to determine the 3He density inside of the target with great precision. Historically, we understood the width of these lines would be dependent on the temperature of the target. Specifically, if I raise the temperature, the width should get bigger. I found that was not the case, which was very confusing at first, though very exciting now that I realize the data are self-consistent and suggestive of unexpected behavior. This thesis details the development of high quality, glass, polarized 3He targets for the 2020 An 1 /dn 2 and 2023 Gn E experiments, which utilized the first 3He convection targets and broke records in target quality. This thesis also covers the initial development of metal windows for the next-generation of 3He target-cells. Finally, this thesis documents the temperature dependence of the width of potassium (K) and rubidium (Rb) absorption lines as measured with laser spectroscopy.
The gravity fields of celestial bodies that possess an atmosphere are periodically perturbed by the redistribution of fluid mass associated with the atmospheric dynamics. A component of this perturbation is due to the gravitational response of the body to the deformation of its surface induced by the atmospheric pressure loading. The magnitude of this effect depends on the relation between the loading and the response in terms of geopotential variations measured by the load Love numbers. In this work, we simulate and analyze the gravity field generated by the atmospheres of Venus and Mars by accounting for different models of their internal structure. By precisely characterizing the phenomena that drive the mass transportation in the atmosphere through general circulation models, we determine the effect of the interior structure on the response to the atmospheric loading. An accurate estimation of the time-varying gravity field, which measures the atmospheric contribution, may provide significant constraints on the interior structure through the measurement of the load Love numbers. A combined determination of tidal and load Love numbers would enhance our knowledge of the interior of planetary bodies, providing further geophysical constraints in the inversion of internal structure models.The gravity fields of celestial bodies that possess an atmosphere are periodically perturbed by the redistribution of fluid mass associated with the atmospheric dynamics. A component of this perturbation is due to the gravitational response of the body to the deformation of its surface induced by the atmospheric pressure loading. The magnitude of this effect depends on the relation between the loading and the response in terms of geopotential variations measured by the load Love numbers. In this work, we simulate and analyze the gravity field generated by the atmospheres of Venus and Mars by accounting for different models of their internal structure. By precisely characterizing the phenomena that drive the mass transportation in the atmosphere through general circulation models, we determine the effect of the interior structure on the response to the atmospheric loading. An accurate estimation of the time-varying gravity field, which measures the atmospheric contribution, may provide significant constraints on the interior structure through the measurement of the load Love numbers. A combined determination of tidal and load Love numbers would enhance our knowledge of the interior of planetary bodies, providing further geophysical constraints in the inversion of internal structure models.
The Cassini mission has provided measurements of the gravity of several moons of Saturn, as well as an estimate of the tidal response, expressed as the degree 2 Love number k 2 , of its largest moon, Titan. The first estimates of Titan’s Love number were larger than pre-Cassini expectations. Interior modeling suggested it may be explained with a dense ocean, but interpretation remained unclear. We have analyzed Cassini tracking data to determine Titan’s gravity field and its Love number. Our gravity results are consistent with earlier studies, but we find a lower Love number for Titan of k 2 =0.375±0.06. This lower value follows from an elaborate investigation of the tidal effects. We show that a dense ocean is not implied by the obtained Love number; instead, a water or ammonia ocean is more likely. A lower density ocean can increase the likeliness of contact between the silicate core and ocean, which can leach minerals into the ocean and could promote its habitability.
SUMMARY In this work, we present both 1-D and 3-D shear wave velocity (Vs) models of the oceanic crust and uppermost mantle below the Deep OCean Test ARray area, located ∼ 70 km north of the central section of the Gloria Fault, in the eastern North-Atlantic Ocean. The velocity models are inferred from the dispersion of surface waves recorded on ocean bottom seismometers. Dispersion measurements are obtained from the analysis of ambient seismic noise at short periods (< 14 s) and teleseismic surface waves at long periods (> 14 s) using the two-station method. The 1-D Vs model is inferred from the joint inversion of Rayleigh wave phase velocities and Love wave group and phase velocities. The 3-D tomographic model is obtained by inversion of 2-D Love wave group velocity maps as a function of depth, further constrained by the average of Love wave phase velocities obtained from ambient noise (4–9 s) and the average Rayleigh and Love wave phase velocities calculated from teleseismic data (14–44 s). The 1-D Vs model shows a sediment layer with a low velocity of 1.05 km s−1, similar to previous studies in the region. Below the sediments, we find an oceanic crust with velocities ranging from 3.3 to 4.5 km s−1. The model reaches an unusually high velocity of 4.9 km s−1 in a 20 km thick layer at depths between 16 and 36 km. We interpret this fast velocity layer as indicative of the presence of harzburgite, a residue of enhanced melting that might have been formed by the proximity between the Mid-Atlantic Ridge and the Azores mantle plume. At greater depths the velocity decreases, forming a low-velocity zone that reaches a minimum at ∼ 70 km depth, which we interpret as the maximum depth for the lithosphere–asthenosphere boundary. The 3-D model shows a structure that is mostly horizontally layered, with Vs isocontours at 3.5–4.5 km s−1 highlighting oscillations of the crustal structure with wavelengths of ∼25–30 km. These oscillations may be due to changes in the rate of mantle upwelling and magma supply rate.
Effective tidal Love numbers and phase angles for the O sub one, K sub one, M sub two, K sub two, P sub one, and S sub two, tides are recovered. The effective tidal phase angles tend to be on the order of a few degrees. The effective tidal Love numbers are generally less than the solid earth Love number K sub two, of about 0.30. This supports the contention that the ocean tides give an apparent depression of the solid earth Love number. Ocean tide amplitudes and phases are calculated for the above tides assuming K sub two = 0.30 and the solid earth lag angle O sub two = 0. The results show good agreement on GEOS-1 but not on GEOS-II.
Variations in rotation and orientation of the Moon are sensitive to solid-body tidal dissipation, dissipation due to relative motion at the fluid-core/ solid-mantle boundary, and tidal Love number k2. There is weaker sensitivity to flattening of the core-mantle boundary (CMB) and fluid core moment of inertia. Accurate Lunar Laser Ranging (LLR) measurements of the distance from observatories on the Earth to four retroreflector arrays on the Moon are sensitive to lunar rotation and orientation variations and tidal displacements. Past solutions using the LLR data have given results for dissipation due to solid-body tides and fluid core plus Love number. Past detection of CMB flattening has been marginal but is improving, while direct detection of the core moment has not yet been achieved. Three decades of Lunar Laser Ranging (LLR) data are analyzed using a weighted least-squares approach. The lunar solution parameters include dissipation at the fluid-core/solid-mantle boundary, tidal dissipation, dissipation-related coefficients for rotation and orientation terms, potential Love number k2, a correction to the constant term in the tilt of the equator to the ecliptic which is meant to approximate the influence of core-mantle boundary flattening, and displacement Love numbers h2 and l2. Several solutions, with different combinations of solution parameters and constraints, are considered.
ABSTRACT We carefully develop the framework required to model the dynamical tidal response of a spinning neutron star in an inspiralling binary system, in the context of Newtonian gravity, making sure to include all relevant details and connections to the existing literature. The tidal perturbation is decomposed in terms of the normal oscillation modes, used to derive an expression for the effective Love number which is valid for any rotation rate. In contrast to previous work on the problem, our analysis highlights subtle issues relating to the orthogonality condition required for the mode-sum representation of the dynamical tide and shows how the prograde and retrograde modes combine to provide the overall tidal response. Utilizing a slow-rotation expansion, we show that the dynamical tide (the effective Love number) is corrected at first order in rotation, whereas in the case of the static tide (the static Love number) the rotational corrections do not enter until second order.
Relations between neutron star properties that do not depend on the nuclear equation of state offer insights on neutron star physics and have practical applications in data analysis. Such relations are obtained by fitting to a range of phenomenological or nuclear physics equation of state models, each of which may have varying degrees of accuracy. In this study we revisit commonly used relations and reassess them with a very flexible set of phenomenological nonparametric equation of state models that are based on Gaussian processes. Our models correspond to two sets: equations of state which mimic hadronic models, and equations of state with rapidly changing behavior that resemble phase transitions. Here we quantify the accuracy of relations under both sets and discuss their applicability with respect to expected upcoming statistical uncertainties of astrophysical observations. We further propose a goodness-of-fit metric which provides an estimate for the systematic error introduced by using the relation to model a certain equation-of-state set. Overall, the nonparametric distribution is more poorly fit with existing relations, with the I–Love–Q relations retaining the highest degree of universality. Fits degrade for relations involving the tidal deformability, such as the binary-Love and compactness-Love relations, and when introducing phase transition phenomenology. For most relations, systematic errors are comparable to current statistical uncertainties under the nonparametric equation of state distributions.
Block Encoding (BE) is a crucial subroutine in many modern quantum algorithms, including those with near-optimal scaling for simulating quantum many-body systems, which often rely on Quantum Signal Processing (QSP). Currently, the primary methods for constructing BEs are the Linear Combination of Unitaries (LCU) and the sparse oracle approach. In this work, we demonstrate that QSP-based techniques, such as Quantum Singular Value Transformation (QSVT) and Quantum Eigenvalue Transformation for Unitary Matrices (QETU), can themselves be efficiently utilized for BE implementation. Specifically, we present several examples of using QSVT and QETU algorithms, along with their combinations, to block encode Hamiltonians for lattice bosons, an essential ingredient in simulations of high-energy physics. We also introduce a straightforward approach to BE based on the exact implementation of Linear Operators Via Exponentiation and LCU (LOVE-LCU). We find that, while using QSVT for BE results in the best asymptotic gate count scaling with the number of qubits per site, LOVE-LCU outperforms all other methods for operators acting on up to qubits, highlighting the importance of concrete circuit constructions over mere comparisons of asymptotic scalings. Using LOVE-LCU to implement the BE, we simulate the time evolution of single-site and two-site systems in the lattice theory using the Generalized QSP algorithm and compare the gate counts to those required for Trotter simulation.
Long period records of multiple Love waves from the 1957 earthquake in Mongolia at Pasadena are analyzed and compared to synthetic seismograms, generated by the method of Kanamori. A fit in the time domain shows that the records are not consistent with the previous solution, achieved through a frequency domain analysis of directivity. The solution asks for a shorter rupture of 270 km at a velocity of 3.5 km/s. The focal parameters are constrained by updating all the reported first motion and are found to be: Strike = 103 deg, Dip = 53 deg, Slip = 32 deg. A seismic moment of 1.8 10 to the 28th power dynes-cm is obtained. These figures are also consistent with a time domain analysis of Love waves at Palisades and Strasbourg, and of Rayleigh waves at Pasadena, with a directivity study of Love waves at Pasadena, and with static deformation and isoseismal data. A discussion is given of the relation between moment, magnitude and rupture area, and a comparison is made with other events in the same region: It is concluded that this earthquake does not exhibit an intra-plate behavior, but rather compares better with inter-plate events, such as the great Assam earthquake.
The global lateral heterogeneity of the upper mantle is investigated using the classical Fourier-transform method of Sato(1958) and IDA/GDSN data from 25 1980 earthquakes. The great-circle phase velocities of 200 Love and 250 Rayleigh 100-330-sec-period fundamental-mode wave paths are determined and interpreted in terms of regional phase-velocity variation, using additional data on surface tectonics to extrapolate odd-harmonic information from the even-harmonic data. The results are presented in extensive tables, maps, and graphs. Regionalized inversion using the seven-region model of Okal (1977) is found to give maximum variance reductions of 65 percent for Love waves and 85 percent for Rayleigh waves, compared to 60 and 90 percent for l(max) = 2 inversion. Significant interregion differences are found in the regionalized Love-wave phase velocities.
Laser ranges between observatories on the Earth and retroreflectors on the Moon started in 1969 and continue to the present. Recent range accuracies are 2 cm while earliest ranges are an C, order of magnitude less certain. Four retroreflectors are ranged: three located at the Apollo 11, 14, and 15 sites and one on the Lunakhod 2 rover. Accurate analysis of the range data determines a number of lunar science parameters. The lunar interior variables include a fluid core parameter. The Lunar Laser Ranging effort is reviewed elsewhere. Many parameters are detected through their influence on rotation. Also detected are solid-body tides and accurate selenocentric reflector locations. Determined through the rotation are moment-of-inertia differences, gravitational harmonics, potential Love number, and dissipation effects due to tides and molten core. The rotation of the Moon is not at its minimum energy state; some recently active process has caused free librations. The moment differences contributed to the recent improvement of the Moon's moment of inertia from the Lunar Prospector gravity field. The Love numbers provide bulk elastic properties. Future possibilities for measurement include oblateness of the core-mantle boundary and core moment. A study of dissipation signatures in the rotation determines tidal Q vs. frequency and concludes that the Moon has a molten core. At 1 month the tidal Q is 37 and at 1 yr it is 60. The core radius is < or = 352 km for Fe and < or = 374 km for the Fe-FeS eutectic. The core detection exceeds 3x its uncertainty. The spin of the core is not aligned with the spin of the mantle and torque arises from the velocity difference at the boundary. Yoder's turbulent boundary layer theory is used to compute the radii. The present heat generation from tides and core interaction is minor compared to radiogenic heating. The heating for ancient times is more interesting. Peale and Cassen investigated lunar tidal heating while the lunar orbit expanded due to tides on Earth. Their calculations predate the measurement of Q and should be multiplied by 3.45 to match the lunar-laser-determined Love number and monthly Q. Tidal-heating computations depend on how fast the lunar orbit evolved and whether the tidal dissipation is localized. Neither is known, but plausible assumptions lead to early central region temperature increases of several hundred degrees. Most of the energy is deposited early in the Moon's history. The turbulent boundary layer theory allows a prediction of energy dissipated at the core-mantle boundary during orbit evolution. Under the assumption that the properties of the early core are the same as at present, the energy dissipated by core-mantle interaction is about the same as for tidal dissipation, but it is deposited in a smaller volume. This source of energy is capable of promoting convection in an early fluid core and driving a dynamo. This is a transient phase with a duration depending on the rate of orbit evolution. Plausible assumptions lead to a duration of a few hundred million years. Thus, the remnant magnetization of many lunar rocks is compatible with a brief global magnetic field powered by dynamical energy dissipation. Analysis of the lunar laser ranges is providing information on lunar geophysics. Future data will improve accuracies of present solution parameters, and several more interior effects should be detectable.
We have analyzed Ka‒band range rate (KBRR) and Deep Space Network (DSN) data from the Gravity Recovery and Interior Laboratory (GRAIL) primary mission (1 March to 29 May 2012) to derive gravity models of the Moon to degree 420, 540, and 660 in spherical harmonics. For these models, GRGM420A, GRGM540A, and GRGM660PRIM, a Kaula constraint was applied only beyond degree 330. Variance‒component estimation (VCE) was used to adjust the a priori weights and obtain a calibrated error covariance. The global root‒mean‒square error in the gravity anomalies computed from the error covariance to 320×320 is 0.77 mGal, compared to 29.0 mGal with the pre‒GRAIL model derived with the SELENE mission data, SGM150J, only to 140×140. The global correlations with the Lunar Orbiter Laser Altimeter‒derived topography are larger than 0.985 between l = 120 and 330. The free‒air gravity anomalies, especially over the lunar farside, display a dramatic increase in detail compared to the pre‒GRAIL models (SGM150J and LP150Q) and, through degree 320, are free of the orbit‒track‒related artifacts present in the earlier models. For GRAIL, we obtain an a posteriori fit to the S‒band DSN data of 0.13 mm/s. The a posteriori fits to the KBRR data range from 0.08 to 1.5 micrometers/s for GRGM420A and from 0.03 to 0.06 micrometers/s for GRGM660PRIM. Using the GRAIL data, we obtain solutions for the degree 2 Love numbers, k20=0.024615+/-0.0000914, k21=0.023915+/-0.0000132, and k22=0.024852+/-0.0000167, and a preliminary solution for the k30 Love number of k30=0.00734+/-0.0015, where the Love number error sigmas are those obtained with VCE.
We present a spherical harmonic solution of the static gravity field of Mars to degree and order 120, GMM-3, that has been calculated using the Deep Space Network tracking data of the NASA Mars missions, Mars Global Surveyor (MGS), Mars Odyssey (ODY), and the Mars Reconnaissance Orbiter (MRO). We have also jointly determined spherical harmonic solutions for the static and time-variable gravity field of Mars, and the Mars k(sub 2) Love numbers, exclusive of the gravity contribution of the atmosphere. Consequently, the retrieved time-varying gravity coefficients and the Love number k(sub 2) solely yield seasonal variations in the mass of the polar caps and the solid tides of Mars, respectively. We obtain a Mars Love number k(sub 2) of 0.1697 +/- 0.0027 (3- sigma). The inclusion of MRO tracking data results in improved seasonal gravity field coefficients C(sub 30) and, for the first time, C 50. Refinements of the atmospheric model in our orbit determination program have allowed us to monitor the odd zonal harmonic C(sub 30) for approximately 1.5 solar cycles (16 years). This gravity model shows improved correlations with MOLA topography up to 15% larger at higher harmonics ( l = 60-80) than previous solutions.
The aubrites are a group of differentiated meteorites that formed in extremely reducing conditions, with oxygen fugacities (ƒO2) ranging from ~2 to ~6 log units below the Iron-Wüstite buffer. At these extreme conditions, elements that are lithophile (silica-loving) on Earth can behave as chalcophiles (sulfur-loving) or siderophiles (metal-loving), and FeO-poor silicates and exotic sulfides can form. Elemental partitioning among minerals at these conditions are still not well understood, thus studying aubrites could help better constrain elemental behavior. Only 30 aubrites exist; however, they display various textures, which can be difficult to identify in small samples. Identifying composite clasts can help in understanding the igneous history of the aubrite parent bodies. In order to distinguish different minerals and textures in larger samples, we use X-ray computed tomography (XCT), which is a useful, non-destructive analysis that can produce a 3D representation of a meteorite's textures, structures, and modal mineralogy. This study investigates the Norton County aubrite using XCT. Norton County is a fragmental impact breccia aubrite, and was an observed fall with a main mass of 1.1 tons. This large amount of material offers an opportunity to investigate a great volume of reduced, aubritic sample and study a more diverse variety of clasts. Here we report XCT results of two samples of Norton County (NC 15417) in order to constrain the 3D modal mineralogy of silicates, sulfides, and metals, and to identify unique clasts within the matrix.