The Maxwell-Pauli Equations

We study the quantum mechanical many-body problem of $N \geq 1$ non-relativistic electrons with spin interacting with their self-generated classical electromagnetic field and $K \geq 0$ static nuclei. We model the dynamics of the electrons and their self-generated electromagnetic field using the so-called many-body Maxwell-Pauli equations. The main result of this thesis is to construct time global, finite-energy, weak solutions to the many-body Maxwell-Pauli equations under the assumption that the fine structure constant $\alpha$ and the nuclear charges are not too large. The assumptions on the size of $\alpha$ and the nuclear charges ensure that we have energetic stability for this system, i.e., the absolute ground state energy exists. The work in this thesis serves as an initial step towards understanding the connection between the energetic stability of matter in quantum mechanics and the well-posedness of the corresponding dynamical equations.Comment: 95 pages. PhD thesis, Georgia Institute of Technology, May 2020. Includes results from arXiv:1904.0674

United States v. Robinson

This article provides an overview of fourth amendment litigation that focused on the question of what constitutes an “unreasonable” search. The Supreme Court had previously provided guidance in Terry v. Ohio and Chimel v. California. This article provides a brief overview of these cases, and then it turns to more thoroughly examine the decision in US v. Robinson

Star-Disk Collisions in the Galactic Center

Recent observations of the Galactic Center (GC) have revealed that there is a relative paucity of Red Giant (RG) stars within the central parsec. However, these observations conflict with our current theoretical understanding. We would expect the GC to have formed a segregated cusp of late-type stars. A recent explanation for this theoretical issue is that the outer envelopes of RG stars may have been stripped due to collisions with a fragmenting accretion disk in the GC. Both numerical and analytic models of star-disk collisions have been considered by several authors prior to this work, but a majority of the literature has focused on either the envelope stripping of a Main-Sequence (MS) star or other phenomena associated with this particular interaction. Here we investigate the envelope stripping of a RG star of radius R* = 10 R and mass M* = 1M colliding with the dense regions of a fragmenting disk. From our simulations, we are able to conclude that a RG star is likely to be stripped of its outer envelope and, occasionally, disrupted.Undergraduat

Differences between proposed Apollo sites: 1. Synthesis

Recent observations of the spectral reflectivity and emissivity of the five prime Apollo landing sites are evaluated in the context of similar observations of other localities on the moon and of data returned from unmanned lunar probes. We conclude that those five sites differ significantly only in minor constituents and/or relative valence states and that those differences are more modest than the differences that characterize mare regions generally. Recommendations of priorities for the five prime Apollo sites are made based on their uniqueness for sample return. Sampling of other lunar localities displaying anomalous emissivities and extreme color differences will be required to ascertain the full range of lithologies that constitute the lunar surface

Transmission and Storage Rates for Sequential Massive Random Access

This paper introduces a new source coding paradigm called Sequential Massive Random Access (SMRA). In SMRA, a set of correlated sources is encoded once for all and stored on a server, and clients want to successively access to only a subset of the sources. Since the number of simultaneous clients can be huge, the server is only allowed to extract a bitstream from the stored data: no re-encoding can be performed before the transmission of the specific client's request. In this paper, we formally define the SMRA framework and introduce both storage and transmission rates to characterize the performance of SMRA. We derive achievable transmission and storage rates for lossless source coding of i.i.d. and non i.i.d. sources, and transmission and storage rates-distortion regions for Gaussian sources. We also show two practical implementations of SMRA systems based on rate-compatible LDPC codes. Both theoretical and experimental results demonstrate that SMRA systems can reach the same transmission rates as in traditional point to point source coding schemes, while having a reasonable overhead in terms of storage rate. These results constitute a breakthrough for many recent data transmission applications in which different parts of the data are requested by the clients

Variability of the methane trapping in martian subsurface clathrate hydrates

Recent observations have evidenced traces of methane CH4 heterogeneously distributed in the martian atmosphere. However, because the lifetime of CH4 in the atmosphere of Mars is estimated to be around 300-600 years on the basis of photochemistry, its release from a subsurface reservoir or an active primary source of methane have been invoked in the recent literature. Among the existing scenarios, it has been proposed that clathrate hydrates located in the near subsurface of Mars could be at the origin of the small quantities of the detected CH4. Here, we accurately determine the composition of these clathrate hydrates, as a function of temperature and gas phase composition, by using a hybrid statistical thermodynamic model based on experimental data. Compared to other recent works, our model allows us to calculate the composition of clathrate hydrates formed from a more plausible composition of the martian atmosphere by considering its main compounds, i.e. carbon dioxyde, nitrogen and argon, together with methane. Besides, because there is no low temperature restriction in our model, we are able to determine the composition of clathrate hydrates formed at temperatures corresponding to the extreme ones measured in the polar caps. Our results show that methane enriched clathrate hydrates could be stable in the subsurface of Mars only if a primitive CH4-rich atmosphere has existed or if a subsurface source of CH4 has been (or is still) present.Comment: Accepted for publication in Planetary and Space Scienc

Improving global accessibility to offshore wind power through decreased operations and maintenance costs: a hydrodynamic analysis

Improved access to renewable energy in developing economies will be a major factor in future global efforts to reduce CO2 emissions, while simultaneously raising living conditions in areas presently without or with only limited access to electricity. Coastal populations stand to benefit greatly from reduced costs of offshore wind farms, which are one of the fastest growing and most economical sources of marine renewable energy. A considerable drawback of offshore wind power is the high cost of operations and maintenance (O&M), which can account for 25-50% of total energy production costs. Present-day maintenance procedures, using crew transfer vessels, rely on the significant wave height (HS) as the limiting factor by which to decide whether or not it is safe to access the offshore turbines. In practice, HS has to be applied conservatively, thus raising the costs through increased downtime. A method is proposed here with the objective of reducing overall costs through improved analysis of the motion of the crew transfer vessels (CTVs) used to transport repair technicians onto offshore wind turbine structures. CTV motion depends on the hydrodynamic forces incident on the vessel under operating conditions and the effect that the presence of the turbine has on the flow field. A change in the hydrodynamic field caused by the turbine monopile can cause a vessel abutted against the turbine support column to lose frictional contact and slip. Using the open-source computational fluid dynamics software, OpenFOAM, and in situ experimental results, the diffracted surface elevation and a wave kinematics model for the near-wake of a turbine monopile are presented. More accurate estimates of significant wave height and wave kinematics incident on a vessel close to a turbine monopile will facilitate much improved analysis of vessel motions under operational conditions