On the Spectra of Real and Complex Lam\'e Operators

We study Lam\'e operators of the form $$L = -\frac{d^2}{dx^2} + m(m+1)\omega^2\wp(\omega x+z_0),$$ with $m\in\mathbb{N}$ and $\omega$ a half-period of $\wp(z)$. For rectangular period lattices, we can choose $\omega$ and $z_0$ such that the potential is real, periodic and regular. It is known after Ince that the spectrum of the corresponding Lam\'e operator has a band structure with not more than $m$ gaps. In the first part of the paper, we prove that the opened gaps are precisely the first $m$ ones. In the second part, we study the Lam\'e spectrum for a generic period lattice when the potential is complex-valued. We concentrate on the $m=1$ case, when the spectrum consists of two regular analytic arcs, one of which extends to infinity, and briefly discuss the $m=2$ case, paying particular attention to the rhombic lattices

Probing the Interstellar Medium on AU Size Scales Using Pulsar Scintillation

We have used pulsar scintillation observations to probe the ionized component of the interstellar medium on AU size scales. Previous work had shown that the presence of scintillation arcs in pulsar secondary spectra requires that the scattering along the line of sight to the pulsar is dominated by a thin screen of scattering material. An isotropic image gives rise to a sharply delineated arc, while an anisotropic image with refractive hot spots elongated along the pulsar velocity vector gives rise to detailed substructure and arclets in the secondary spectrum. Twenty-five years of archival scintillation data from the Arecibo Observatory show that arclets are present in ~ 25% of low radio frequency observations of PSR B0834+06 and PSR B1133+16 and that the decorrelation time scale of substructure is ~ 6 months. Observations of the pulsar PSR B0834+06 at Arecibo identified four isolated arclets at high delays. These arclets were present throughout a month of observations, and their angular separation from the pulsar changed over the course of the month in a linear fashion. This transverse motion is dominated by the velocity of the pulsar and implies an approximate upper limit to the screen velocity of 7 km s-1. We applied a plasma lens model to these observations assuming that the high delay arclets are caused by refracting plasma lenses in the scattering screen. We place an upper bound of a ~ 0.1 AU on the lens size and estimate an electron density within the lens of ne ~ 200 cm-3. The ionized component of the lens thus has a mass of Ml ~ 10-18 Msun. These parameters are very similar to the predicted parameters for the plasma lenses thought to cause Extreme Scattering Events in quasars

Graduate Recital: Alexander Hill

Kemp Recital HallApril 2, 2016Saturday Evening5:30 p.m

THE EFFECT OF PRETREATMENT METHODS ON METHANE YIELD AND NUTRIENT SOLUBILIZATION DURING ANAEROBIC DIGESTION OF MICROALGAE

Microalgal biomass is a candidate feedstock for biofuel production. To improve the sustainability of algae biofuel production, following biofuel recovery, the biomass nutrients should be recycled for additional algae growth. Anaerobic digestion of algae or oil-extracted algae is a means of recovering carbon and other nutrients, while offsetting algae production electricity demand. The major limiting factor in microalgae digestion is the low biodegradability of the cell walls. In the present study, various pretreatment technologies were tested at bench scale for their ability to improve raw, non-lipid-extracted algae biodegradability, which was assessed in terms of methane yield, volatile solids destruction, and solubilization of N, P, and K. The microalgae were harvested by sedimentation from outdoor wastewater-fed raceways ponds operated in coastal southern California. Four pretreatment methods (sonication, high-pressure homogenization, autoclaving, and boiling) were used on the algae slurries, each followed by batch anaerobic digestion (40 days at 35oC). Biomass sonication for 10 minutes showed the highest methane yield of 0.315 L CH4/ g VSIN, which is a 28% increase over the untreated control. Conversely, autoclaved algae slurry inhibited methane production (0.200 vs. 0.228 L CH4/ g VSIN for the treatment and control). A preliminary energy balance indicated that none of the pretreatments led to a net increase in energy conversion to biomethane. However, pretreatment did increase the initial N and P solubilization rates, but, after digestion, the ultimate N and P solubilization was nearly the same among the treatments and controls. After 40 days of digestion, solubilization of N, P, and K reached, respectively, 50-60% of average total Kjeldahl N, 40-50% of average total P, and 80-90% of average total K. Descriptive first-order models of solubilization were developed. Overall, certain pretreatments marginally improved methane yield and nutrient solubilization rate, which cast doubt on the efficacy of, or even the need for, algae biomass pretreatment prior to anaerobic digestion

Emission, dispersion and local deposition of ammonia volatilised from farm buildings and following the application of cattle slurry to grassland

Merged with duplicate record 10026.1/570 on 15.02.2017 by CS (TIS)Emissions of ammonia (NH3) into the atmosphere, principally from agricultural sources, have been implicated in the pollution of forests, moorlands and grasslands, through the subsequent deposition of reduced nitrogen (NHx -N). Consequently, legislation has been implemented to control both the transboundary transport and local environmental impacts of NHx. This thesis investigates the emission, dispersion and local deposition of NH3 from two sources that are major components of national NH3 emissions inventories, slurry applied to grassland and naturally ventilated cattle buildings. A N balance method was identified for determining the time-average deposition of NH3 downwind of a farm building, whilst an adapted micrometeorological flux-gradient technique was developed for estimating local deposition downwind of slurry spreading. This method used an analytical atmospheric dispersion model to provide advection corrections to the standard flux-gradient method. The UK-ADMS model, which incorporates a reasonably detailed treatment of building effects, was identified for use in determining the near-field dispersion from naturally ventilated farm buildings. Eight field experiments were conducted to determine the emission, dispersion and local deposition of NH3 volatilised from slurry applications. Emission fluxes during the initial runs following slurry spreading were found to depend on friction velocity, relative humidity and rainfall. Local deposition, at sufficient rates to affect local deposition budgets, was not found to occur during near-freezing conditions or following the application of fertilisers. Local deposition velocities during other periods were found to depend on the latent heat flux, temperature and the roughness length. During such periods, 14 - 18 % of the emitted NH3 was estimated to deposit within 50 m of the source. Experiments were also conducted at two naturally ventilated farm buildings, the Silsoe Research Institute Structures Building and a working dairy farm. Ammonia emission factors were determined for the main building and slurry lagoon at the dairy farm. A novel application of a model back-calculation method was applied to determine the emission from the lagoon. Dispersion of NH3 from both sites was found to be adequately modelled using UK-ADMS. Approximately 2 % of the emitted NH3 deposited within 100 - 150 m of each building. Time averaged deposition velocities calculated from the farm building studies confirmed that NH3 was deposited to the leaf surfaces and uptaken across the leaf cuticle. Temperature dependent exchange rates were also indicated by the results of the farm building experiments, with NH3 uptake being regulated by the assimilation potential of the plant. The experimental results demonstrated that deposition around both sources could lead to local critical load exceedances. These were only estimated to occur within a few tens of metres downwind of slurry spreading whilst critical load exceedances were predicted at distances of up to 100 m or more downwind of the farm building. The temporal variability in local recapture found in these experiments, particularly for farm buildings, suggests that seasonal variability in the treatment of NH3 emission and deposition should be included in atmospheric transport models. Furthermore, it is possible that transboundary transport of NHx may increase during winter periods with peak housing emissions.The Institute of Grassland and Environmental Researc

Power Corrections to the Universal Heavy WIMP-Nucleon Cross Section

WIMP-nucleon scattering is analyzed at order $1/M$ in Heavy WIMP Effective Theory. The $1/M$ power corrections, where $M\gg m_W$ is the WIMP mass, distinguish between different underlying UV models with the same universal limit and their impact on direct detection rates can be enhanced relative to naive expectations due to generic amplitude-level cancellations at leading order. The necessary one- and two-loop matching calculations onto the low-energy effective theory for WIMP interactions with Standard Model quarks and gluons are performed for the case of an electroweak SU(2) triplet WIMP, considering both the cases of elementary fermions and composite scalars. The low-velocity WIMP-nucleon scattering cross section is evaluated and compared with current experimental limits and projected future sensitivities. Our results provide the most robust prediction for electroweak triplet Majorana fermion dark matter direct detection rates; for this case, a cancellation between two sources of power corrections yields a small total $1/M$ correction, and a total cross section close to the universal limit for $M \gtrsim {\rm few} \times 100\,{\rm GeV}$. For the SU(2) composite scalar, the $1/M$ corrections introduce dependence on underlying strong dynamics. Using a leading chiral logarithm evaluation, the total $1/M$ correction has a larger magnitude and uncertainty than in the fermionic case, with a sign that further suppresses the total cross section. These examples provide definite targets for future direct detection experiments and motivate large scale detectors capable of probing to the neutrino floor in the TeV mass regime.Comment: 12 pages, 4 figures; references added, XENONnT projection included, version to appear in Physics Letters

The range of axial rotation of the glenohumeral joint.

Accepted versio