Induced subarrays of Latin squares without repeated symbols

We show that for any Latin square L of order 2m, we can partition the rows and columns of L into pairs so that at most (m+3)/2 of the 2x2 subarrays induced contain a repeated symbol. We conjecture that any Latin square of order 2m (where m ≥ 2, with exactly five transposition class exceptions of order 6) has such a partition so that every 2x2 subarray induced contains no repeated symbol. We verify this conjecture by computer when m ≤ 4

DETERMINING PHYSICAL CONDITIONS IN STAR FORMING REGIONS

This dissertation is a study of the physical conditions in star-forming regions, and combines observational data and theoretical calculations. We studied the physical conditions of Orions Veil, which is an absorbing screen that lies along the line of sight to the Orion H II region. We computed photoionization models of the Veil. We combined calculations with UV, radio, and optical spectra that resolve the Veil into two velocity components. We derive many physical parameters for each component seen in 21 cm absorption. We find the magnetic field energy dominates turbulent and thermal energies in one component while the other component is close to equipartition between turbulent and magnetic energies. We observe H2 absorption for highly excited levels. We find that the low ratio of H2/H0 in the Veil is due to the high UV flux incident upon the Veil. We detect blueshifted S+2 and P+2 ions which must arise from ionized gas between the neutral portions of the Veil and the Trapezium and shields the Veil from ionizing radiation. We determine the ionized and neutral layers of the Veil will collide in less than 85,000 years. The second part of this dissertation involved self-consistently calculating the thermal and chemical structure of an H II region and photodissociation region (PDR) that are in pressure equilibrium. This differs from previous work, which used separate calculations for each gas phase. Our calculations span a wide range of initial conditions. We describe improvements made to the spectral synthesis code Cloudy which made these calculations possible. These include the addition of a molecular network with ~1000 reactions involving 68 molecules and improved treatment of the grain physics. Archival data are used to derive important physical characteristics of observed H II regions and PDRs. These include stellar temperatures, electron densities, ionization parameters, UV flux, and PDR density. The contribution of the H II region to PDR emission line diagnostics is also calculated. Finally, these calculations are used to derive emission line ratios than can tell us the equation of state in star-forming regions

Herschel dust emission as a probe of starless cores mass: MCLD 123.5+24.9 of the Polaris Flare

We present newly processed archival Herschel images of molecular cloud MCLD 123.5+24.9 in the Polaris Flare. This cloud contains five starless cores. Using the spectral synthesis code Cloudy, we explore uncertainties in the derivation of column densities, hence, masses of molecular cores from Herschel data. We first consider several detailed grain models that predict far-IR grain opacities. Opacities predicted by the models differ by more than a factor of two, leading to uncertainties in derived column densities by the same factor. Then we consider uncertainties associated with the modified blackbody fitting process used by observers to estimate column densities. For high column density clouds (N(H) $\gg$ 10$^{22}$ cm$^{-2}$), this fitting technique can underestimate column densities by about a factor of three. Finally, we consider the virial stability of the five starless cores in MCLD 123.5+24.9. All of these cores appear to have strongly sub-virial masses, assuming, as we argue, that $^{13}$CO line data provide reliable estimates of velocity dispersions. Evidently, they are not self-gravitating, so it is no surprise that they are starless.Comment: ApJ, Accepted. Minor typographical errors corrected and figures 6 & 7 updated in v

Quantum computing for quantum tunneling

We demonstrate how quantum field theory problems can be practically encoded by using a discretization of the field theory problem into a general Ising model, with the continuous field values being encoded into Ising spin chains. To illustrate the method, and as a simple proof of principle, we use a (hybrid) quantum annealer to recover the correct profile of the thin-wall tunnelling solution. This method is applicable to many nonperturbative problems

A single step three-strain in vivo Gateway reaction

We developed a simplified, highly efficient Gateway reaction that recombines target DNA to expression (destination) plasmids in vivo and subsequently conjugates the final vector into a recipient strain, all in a single step. This recipient strain does not need to contain any selective marker and can be freely chosen as long as it is sensitive to ccdB counterselection and can be targeted by the RP4α conjugation system. Our protocol is simple, robust, and cost effective. It works in 96-well plate format and performs across a range of temperatures. We designed modular, minimal destination vectors containing a modified Gateway insert to ease vector design by providing locations for insertion of tags, promoters, or conjugations. To demonstrate the utility of our system, we created destination vectors with split adenylate cyclase tags for bacterial two-hybrid (B2H) studies and screened a library of diguanylate cyclases for protein-protein interactions in a single step

Distributed tabulation of flamelet lookup tables

One of the fundamental questions in combustion simulation is how to account for detailed chemistry effects, while controlling both the error of the chemical scheme and the computational cost. Combustion chemistry is important for resolving processes such as flame propagation and pollutant formation, which are non-linear processes that can be computationally expensive. The direct solution of the governing equations of turbulent reacting flows can be prohibitively expensive as the chemical integration is often stiff. Tabulated chemistry methods with flamelet modelling emerge as an alternative to perform direct integration of the chemical source terms and has been extended to a wide range of conditions [1]. In flamelet methods, the chemical time scale is assumed smaller than the time scales of the turbulence, so the flame structure is not affected by the turbulence. In flamelet methods, the thermochemical states of the flame are computed in a preprocessing step, and these values are retrieved from a lookup table loaded into memory at the beginning of the simulation. The flame structure can be recovered through the use of controlling variables, which represent dimensions along the multidimensional space of the flame manifold

Reducing Fretting Corrosion at the Femoral Neck to Taper Junction in Total Hip Arthroplasty

Fretting corrosion due to micromotion between the femoral head and neck of hip implants is a growing concern of surgeons and patients. Debris from corrosion can lead to severe adverse effects for patients of total hip arthroplasty and reduce the lifespan of the product. Previous studies conducted by Zimmer Biomet show a connection between higher impaction force and reduced fretting corrosion and debris. This design project explored this issue and developed a training device using a current technology, a dynamic force sensor, and data analysis software for surgeons to obtain muscle memory of a 4kN strike on the head impactor, which will improve performance in the operating room and reduce the occurrence of fretting corrosion