Products of Eisenstein series and Fourier expansions of modular forms at cusps

We show, for levels of the form $N = p^a q^b N'$ with $N'$ squarefree, that in weights $k \geq 4$ every cusp form $f \in \mathcal{S}_k(N)$ is a linear combination of products of certain Eisenstein series of lower weight. In weight $k=2$ we show that the forms $f$ which can be obtained in this way are precisely those in the subspace generated by eigenforms $g$ with $L(g, 1) \neq 0$. As an application of such representations of modular forms we can calculate Fourier expansions of modular forms at arbitrary cusps and we give several examples of such expansions in the last section.Comment: This is an update to a previous version of the article. In the new version we describe an algorithm (available at https://github.com/michaelneururer/products-of-eisenstein-series) that computes Fourier expansions at cusp

The effect of advance ratio on the aerodynamics of revolving wings

Recent studies have demonstrated that a quasi-steady model closely matches the instantaneous force produced by an insect wing during hovering flight. It is not clear, however, if such methods extend to forward flight. In this study we use a dynamically scaled robotic model of the fruit fly Drosophila melanogaster to investigate the forces produced by a wing revolving at constant angular velocity while simultaneously translating at velocities appropriate for forward flight. Because the forward and angular velocities were constant wing inertia was negligible, and the measured forces can be attributed to fluid dynamic phenomena. The combined forward and revolving motions of the wing produce a time-dependent free-stream velocity profile, which suggests that added mass forces make a contribution to the measured forces. We find that the forces due added mass make a small, but measurable, component of the total force and are in excellent agreement with theoretical values. Lift and drag coefficients are calculated from the force traces after subtracting the contributions due to added mass. The lift and drag coefficients, for fixed angle of attack, are not constant for non-zero advance ratios, but rather vary in magnitude throughout the stroke. This observation implies that modifications of the quasi-steady model are required in order to predict accurately the instantaneous forces produced during forward flight. We show that the dependence of the lift and drag coefficients upon advance ratio and stroke position can be characterized effectively in terms of the tip velocity ratio – the ratio of the chordwise components of flow velocity at the wing tip due to translation and revolution. On this basis we develop a modified quasi-steady model that can account for the varying magnitudes of the lift and drag coefficients. Our model may also resolve discrepancies in past measurements of wing performance based on translational and revolving motion

Concepts of play informing aspects of the design studio

Play is often seen as an unproductive yet structured pastime intended to provide enjoyment to its participants. For young children play is seen as a vital aspect to the learning process, gearing young minds in all aspects of role playing, socialization and understanding the material and making of the world. Play is a conduit for the imagination and though seemingly unproductive sows the seeds for creativity and understanding of the world

Potential Economic Impacts of the Managed Haying and Grazing Provision of CRP

According to the Executive Order 12866, a qualitative and quantitative assessment for any Federal mandate resulting in annual expenditures of $100 million or more is required. This study determines how many of the approximately 34.5 million acres of CRP land is brought back in economic use, how that use is allocated between grazing and haying, and the economic impact.CRP, land allocation, economic impact, Agricultural and Food Policy, Environmental Economics and Policy, Land Economics/Use, Research and Development/Tech Change/Emerging Technologies,

A linear systems analysis of the yaw dynamics of a dynamically scaled insect model

Recent studies suggest that fruit flies use subtle changes to their wing motion to actively generate forces during aerial maneuvers. In addition, it has been estimated that the passive rotational damping caused by the flapping wings of an insect is around two orders of magnitude greater than that for the body alone. At present, however, the relationships between the active regulation of wing kinematics, passive damping produced by the flapping wings and the overall trajectory of the animal are still poorly understood. In this study, we use a dynamically scaled robotic model equipped with a torque feedback mechanism to study the dynamics of yaw turns in the fruit fly Drosophila melanogaster. Four plausible mechanisms for the active generation of yaw torque are examined. The mechanisms deform the wing kinematics of hovering in order to introduce asymmetry that results in the active production of yaw torque by the flapping wings. The results demonstrate that the stroke-averaged yaw torque is well approximated by a model that is linear with respect to both the yaw velocity and the magnitude of the kinematic deformations. Dynamic measurements, in which the yaw torque produced by the flapping wings was used in real-time to determine the rotation of the robot, suggest that a first-order linear model with stroke-average coefficients accurately captures the yaw dynamics of the system. Finally, an analysis of the stroke-average dynamics suggests that both damping and inertia will be important factors during rapid body saccades of a fruit fly

Courtyards and Corners: A New Rural Residential Dwelling

The project further explores the impact of site and circumstance on design as a way of place making and generating concepts. The project is a lakeside rural dwelling that focuses around a tight protected courtyard to the street address, opening to create a corner to the remaining site that fronts a lake

Biologically Inspired Feedback Design for Drosophila Flight

We use a biologically motivated model of the Drosophila's flight mechanics and sensor processing to design a feedback control scheme to regulate forward flight. The model used for insect flight is the grand unified fly (GUF) [3] simulation consisting of rigid body kinematics, aerodynamic forces and moments, sensory systems, and a 3D environment model. We seek to design a control algorithm that will convert the sensory signals into proper wing beat commands to regulate forward flight. Modulating the wing beat frequency and mean stroke angle produces changes in the flight envelope. The sensory signals consist of estimates of rotational velocity from the haltere organs and translational velocity estimates from visual elementary motion detectors (EMD's) and matched retinal velocity filters. The controller is designed based on a longitudinal model of the flight dynamics. Feedforward commands are generated based on a desired forward velocity. The dynamics are linearized around this operating point and a feedback controller designed to correct deviations from the operating point. The control algorithm is implemented in the GUF simulator and achieves the desired tracking of the forward reference velocities and exhibits biologically realistic responses

Quantitative Risk from Fluoroquinolone-Resistant Salmonella and Campylobacter Due to Treatment of Dairy Heifers with Enrofloxacin for Bovine Respiratory Disease

The objective of this study was to evaluate the human health impact of using fluoroquinolones to treat bovine respiratory disease (BRD) in dairy heifers less than 20 months of age. Specifically, this study quantified the probability of persistent symptoms in humans treated with a fluoroquinolone, for a fluoroquinolone-resistant Campylobacter, Salmonella, or multidrug-resistant (MDR) Salmonella infection acquired following the consumption of ground beef. To comply with a Food and Drug Administration requirement for approval of enrofloxacin use in dairy heifers, a binomial event tree was constructed following Food and Drug Administration guidance 152. Release was estimated from the slaughter of dairy cattle carrying fluoroquinolone-resistant bacteria attributed to the proposed use in dairy heifers. For exposure, human foodborne exposure to Campylobacter, Salmonella, and MDR Salmonella after consumption of ground beef was estimated. The consequence assessment included illness, fluoroquinolone treatment, and persistent symptoms in patients treated with a fluoroquinolone. Using best available data to estimate the parameters and probabilities of each event, stochastic simulation was used to represent uncertainty and variability in many of the parameters. A scenario analysis was performed to evaluate the uncertainty of the following parameters: (1) probability of resistance development in treated animals, (2) portion of illnesses attributable to ground beef, and (3) probability of persistent symptoms in patients 18 years of age and over treated with a fluoroquinolone. The population at risk was restricted to people 18 years of age and over, as fluoroquinolones are not labeled for treatment of gastroenteritis in children. The mean annual increased risk of cases in the U.S. population (18 years of age and over) where compromised fluoroquinolone treatment resulted in persistent symptoms was estimated to be 1 in 61 billion (one case every 293 years) for Salmonella, 1 in 33 billion (one case every 158 years) for MDR Salmonella, and 1 in 2.8 billion (one case every 13 years) for Campylobacter