Kondo insulators in the periodic Anderson model: a local moment approach

The symmetric periodic Anderson model is well known to capture the essential physics of Kondo insulator materials. Within the framework of dynamical mean-field theory, we develop a local moment approach to its single-particle dynamics in the paramagnetic phase. The approach is intrinsically non-perturbative, encompasses all energy scales and interaction strengths, and satisfies the low-energy dictates of Fermi liquid theory. It captures in particular the strong coupling behaviour and exponentially small quasiparticle scales characteristic of the Kondo lattice regime, as well as simple perturbative behaviour in weak coupling. Particular emphasis is naturally given to strong coupling dynamics, where the resultant clean separation of energy scales enables the scaling behaviour of single-particle spectra to be obtained.Comment: 15 pages, 10 postscript figures, accepted for publication in EPJ B; HyperTex disable

The Brauer-Manin Obstruction and Sha[2].

We discuss the Brauer-Manin obstruction on del Pezzo surfaces of degree 4. We outline a detailed algorithm for computing the obstruction and provide associated programs in magma. This is illustrated with the computation of an example with an irreducible cubic factor in the singular locus of the defining pencil of quadrics (in contrast to previous examples, which had at worst quadratic irreducible factors). We exploit the relationship with the Tate-Shafarevich group to give new types of examples of Sha[2], for families of curves of genus 2 of the form y^2 = f(x), where f(x) is a quintic containing an irreducible cubic factor

Solar Electric Immersion Heating Element Fabrication

Believing that cooking with flame is cheaper and more efficient than cooking with electricity, Ugandan citizens have exposed themselves to several health and safety risks, including major respiratory issues through harmful emissions, pollution, and the burning down of many homes. Even though solar electric cooking is cheaper and healthier than cooking with flames in the long run, many Ugandans lack the resources to invest in cooking with electricity. The Solar Stove student research team, led by Dr. Pete Schwartz, partnered with Aid Africa to bring solar panels and prototype solar electric cooking units to villages in Uganda. Observing how their product was used over the course of months, the team developed interest in immersion heaters to protect the user, prevent malfunction, and improve efficiency. Iterating on the team’s work, I’ve observed the manufacturing processes for immersion heaters and determined an experiment to find an optimal heater. 2 factors will be examined: insulation with magnesium oxide or gypsum, and heating with Nichrome wire or diodes. Constraints of the design include a $100 budget, a food-grade design, and resources available for manufacturing and assembly in Uganda. Testing has revealed that each arrangement of materials contributes to generally the same level of performance, given current requirements. Deliverables of this project include a detailed manufacturing procedure, data, data analysis of thermal readings at maximum operating conditions (100 Watts), and a quantified recommendation for the best arrangement of immersion heaters

Finite temperature dynamics of the Anderson model

The recently introduced local moment approach (LMA) is extended to encompass single-particle dynamics and transport properties of the Anderson impurity model at finite-temperature, T. While applicable to arbitrary interaction strengths, primary emphasis is given to the strongly correlated Kondo regime (characterized by the T=0 Kondo scale $\omega_{\rm K}$). In particular the resultant universal scaling behaviour of the single-particle spectrum D(\omega; T) \equiv F(\frac{\w}{\omega_{\rm K}}; \frac{T}{\omega_{\rm K}}) within the LMA is obtained in closed form; leading to an analytical description of the thermal destruction of the Kondo resonance on all energy scales. Transport properties follow directly from a knowledge of $D(\omega; T)$. The $T / \omega_{\rm K}$-dependence of the resulting resistivity $\rho(T)$, which is found to agree rather well with numerical renormalization group calculations, is shown to be asymptotically exact at high temperatures; to concur well with the Hamann approximation for the s-d model down to $T/\omega_{\rm K} \sim 1$, and to cross over smoothly to the Fermi liquid form $\rho (T) - \rho (0) \propto -(T/\omega_{\rm K})^2$ in the low-temperature limit. The underlying approach, while naturally approximate, is moreover applicable to a broad range of quantum impurity and related models

Performance of pilot-scale microbial fuel cells treating wastewater with associated bioenergy production in the Caribbean context

Microbial fuel cell (MFC) technology represents a form of renewable energy that generates bioelectricity from what would otherwise be considered a waste stream. MFCs may be ideally suited to the small island developing state (SIDS) context, such as Trinidad and Tobago where seawater as the main electrolyte is readily available and economical renewable and sustainable electricity is also deemed a priority. Hence this project tested two identical laboratory-scaled MFC systems that were specifically designed and developed for the Caribbean regional context. They consisted of two separate chambers, an anaerobic anodic chamber inoculated with wastewater and an aerobic cathodic chamber separated by a proton exchange membrane. Domestic wastewater from two various wastewater treatment plants inflow (after screening) was placed into the anodic chamber, and seawater from the Atlantic Ocean and Gulf of Paria placed into the cathodic chambers respectively with the bacteria present in the wastewater attaching to the anode. Experimental results demonstrated that the bacterial degradation of the wastewaters as substrate induced an electron flow through the electrodes producing bioelectricity whilst simultaneously reducing the organic matter as biochemical oxygen demand and chemical oxygen demand by 30 to 75%. The average bioenergy output for both systems was 84 mW/m² and 96 mW/m² respectively. This study demonstrated the potential for simultaneous bioenergy production and wastewater treatment in the SIDS context