Low-lying zeros of elliptic curve L-functions: Beyond the ratios conjecture

We study the low-lying zeros of L-functions attached to quadratic twists of a given elliptic curve E defined over $\mathbb Q$. We are primarily interested in the family of all twists coprime to the conductor of E and compute a very precise expression for the corresponding 1-level density. In particular, for test functions whose Fourier transforms have sufficiently restricted support, we are able to compute the 1-level density up to an error term that is significantly sharper than the square-root error term predicted by the L-functions Ratios Conjecture.Comment: 33 page

Low-lying zeros of quadratic Dirichlet LL-functions: A transition in the Ratios Conjecture

We study the $1$-level density of low-lying zeros of quadratic Dirichlet $L$-functions by applying the $L$-functions Ratios Conjecture. We observe a transition in the main term as was predicted by the Katz-Sarnak heuristic as well as in the lower order terms when the support of the Fourier transform of the corresponding test function reaches the point $1$. Our results are consistent with those obtained in previous work under GRH and are furthermore analogous to results of Rudnick in the function field case.Comment: 15 page

Low-lying zeros of quadratic Dirichlet LL-functions: Lower order terms for extended support

We study the $1$-level density of low-lying zeros of Dirichlet $L$-functions attached to real primitive characters of conductor at most $X$. Under the Generalized Riemann Hypothesis, we give an asymptotic expansion of this quantity in descending powers of $\log X$, which is valid when the support of the Fourier transform of the corresponding even test function $\phi$ is contained in $(-2,2)$. We uncover a phase transition when the supremum $\sigma$ of the support of $\hat \phi$ reaches $1$, both in the main term and in the lower order terms. A new lower order term appearing at $\sigma=1$ involves the quantity $\hat \phi (1)$, and is analogous to a lower order term which was isolated by Rudnick in the function field case.Comment: 19 page

Interstitial-Scale Modeling of Packed-Bed Reactors

Packed-beds are common to adsorption scrubbers, packed bed reactors, and trickle-bed reactors widely used across the petroleum, petrochemical, and chemical industries. The micro structure of these packed beds is generally very complex and has tremendous influence on heat, mass, and momentum transport phenomena on the micro and macro length scales within the bed. On a reactor scale, bed geometry strongly influences overall pressure drop, residence time distribution, and conversion of species through domain-fluid interactions. On the interstitial scale, particle boundary layer formation, fluid to particle mass transfer, and local mixing are controlled by turbulence and dissipation existing around packed particles. In the present research, a CFD model is developed using OpenFOAM: www.openfoam.org) to directly resolve momentum and scalar transport in both laminar and turbulent flow-fields, where the interstitial velocity field is resolved using the Navier-Stokes equations: i.e. no pseudo-continuum based assumptions. A discussion detailing the process of generating the complex domain using a Monte-Carlo packing algorithm is provided, along with relevant details required to generate an arbitrary polyhedral mesh describing the packed-bed. Lastly, an algorithm coupling OpenFOAM with a linear system solver using the graphics processing unit: GPU) computing paradigm was developed and will be discussed in detail

Insight into High-quality Aerodynamic Design Spaces through Multi-objective Optimization

An approach to support the computational aerodynamic design process is presented and demonstrated through the application of a novel multi-objective variant of the Tabu Search optimization algorithm for continuous problems to the aerodynamic design optimization of turbomachinery blades. The aim is to improve the performance of a specific stage and ultimately of the whole engine. The integrated system developed for this purpose is described. This combines the optimizer with an existing geometry parameterization scheme and a well- established CFD package. The system’s performance is illustrated through case studies – one two-dimensional, one three-dimensional – in which flow characteristics important to the overall performance of turbomachinery blades are optimized. By showing the designer the trade-off surfaces between the competing objectives, this approach provides considerable insight into the design space under consideration and presents the designer with a range of different Pareto-optimal designs for further consideration. Special emphasis is given to the dimensionality in objective function space of the optimization problem, which seeks designs that perform well for a range of flow performance metrics. The resulting compressor blades achieve their high performance by exploiting complicated physical mechanisms successfully identified through the design process. The system can readily be run on parallel computers, substantially reducing wall-clock run times – a significant benefit when tackling computationally demanding design problems. Overall optimal performance is offered by compromise designs on the Pareto trade-off surface revealed through a true multi-objective design optimization test case. Bearing in mind the continuing rapid advances in computing power and the benefits discussed, this approach brings the adoption of such techniques in real-world engineering design practice a ste

Modeling Energy Savings from Urban Shade Trees: An Assessment of the CITYgreen Energy Conservation Module

CITYgreen software has become a commonly used tool to quantify the benefits of urban shade trees. Despite its frequent use, little research has been conducted to validate results of the CITYgreen energy conservation module. The first objective of this study is to perform a familiar application of CITYgreen software to predict the potential energy savings contribution of existing tree canopies in residential neighborhoods during peak cooling summer months. Unlike previous studies utilizing CITYgreen, this study also seeks to assess the software\u27s performance by comparing model results (i.e., predicted energy savings) with actual savings (i.e., savings derived directly from energy consumption data provided by the electric utility provider). Homeowners in an older neighborhood with established trees were found to use less energy for air-conditioning than homeowners in a recently developed site. Results from the assessment of model performance indicated that CITYgreen more accurately estimated the energy savings in the highly vegetated, older neighborhood

Arctic Standards: Recommendations on Oil Spill Prevention, Response, and Safety in the U.S. Arctic Ocean

Oil spilled in Arctic waters would be particularly difficult to remove. Current technology has not been proved to effectively clean up oil when mixed with ice or when trapped under ice. An oil spill would have a profoundly adverse impact on the rich and complex ecosystem found nowhere else in the United States. The Arctic Ocean is home to bowhead, beluga, and gray whales; walruses; polar bears; and other magnificent marine mammals, as well as millions of migratory birds. A healthy ocean is important for these species and integral to the continuation of hunting and fishing traditions practiced by Alaska Native communities for thousands of years.To aid the United States in its efforts to modernize Arctic technology and equipment standards, this report examines the fierce Arctic conditions in which offshore oil and gas operations could take place and then offers a summary of key recommendations for the Interior Department to consider as it develops world-class, Arctic-specific regulatory standards for these activities. Pew's recommendations call for improved technology,equipment, and procedural requirements that match the challenging conditions in the Arctic and for full public participation and transparency throughout the decision-making process. Pew is not opposed to offshore drilling, but a balance must be achieved between responsible energy development and protection of the environment.It is essential that appropriate standards be in place for safety and for oil spill prevention and response in this extreme, remote, and vulnerable ecosystem. This report recommends updating regulations to include Arctic specific requirements and codifying temporary guidance into regulation. The appendixes to this report provide substantially more detail on the report's recommendations, including technical background documentation and additional referenced materials. Please refer to the full set of appendixes for a complete set of recommendations. This report and its appendixes offer guidelines for responsible hydrocarbon development in the U.S. Arctic Ocean