Isogeny graphs of ordinary abelian varieties

Fix a prime number $\ell$. Graphs of isogenies of degree a power of $\ell$ are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse graphs of so-called $\mathfrak l$-isogenies, resolving that they are (almost) volcanoes in any dimension. Specializing to the case of principally polarizable abelian surfaces, we then exploit this structure to describe graphs of a particular class of isogenies known as $(\ell, \ell)$-isogenies: those whose kernels are maximal isotropic subgroups of the $\ell$-torsion for the Weil pairing. We use these two results to write an algorithm giving a path of computable isogenies from an arbitrary absolutely simple ordinary abelian surface towards one with maximal endomorphism ring, which has immediate consequences for the CM-method in genus 2, for computing explicit isogenies, and for the random self-reducibility of the discrete logarithm problem in genus 2 cryptography.Comment: 36 pages, 4 figure

Re-entrant magnetic field induced charge and spin gaps in the coupled dual-chain quasi-one dimensional organic conductor Perylene2_2[Pt(mnt)2_2]

An inductive method is used to follow the magnetic field-dependent susceptibility of the coupled charge density wave (CDW) and spin-Peierls (SP) ordered state behavior in the dual chain organic conductor Perylene$_2$[Pt(mnt)$_2$]. In addition to the coexisting SP-CDW state phase below 8 K and 20 T, the measurements show that a second spin-gapped phase appears above 20 T that coincides with a field-induced insulating phase. The results support a strong coupling of the CDW and SP order parameters even in high magnetic fields, and provide new insight into the nature of the magnetic susceptibility of dual-chain spin and charge systems.Comment: 6 pages, 6 figure

Passive Aeroelastic Tailoring

The Passive Aeroelastic Tailoring (PAT) project was tasked with investigating novel methods to achieve passive aeroelastic tailoring on high aspect ratio wings. The goal of the project was to identify structural designs or topologies that can improve performance and/or reduce structural weight for high-aspect ratio wings. This project considered two unique approaches, which were pursued in parallel: through-thickness topology optimization and composite tow-steering

Cities, The Sharing Economy and What's Next

This report seeks to provide an analysis of what is currently happening in American cities so that city leaders may better understand, encourage and regulate the growing sharing economy. Interviews were conducted with city officials on the impact of the sharing economy and related topics, and the report centers around five key themes: innovation, economic development, equity, safety and implementation.The sharing economy is also commonly referred to as collaborative consumption, the collaborative economy, or the peer-to-peer economy. This term refers to business models that enable providers and consumers to share resources and services, from housing to vehicles and more. These business models typically take the form of an online and/or application-based platform for business transactions

Kinematic Evolution of Simulated Star-Forming Galaxies

Recent observations have shown that star-forming galaxies like our own Milky Way evolve kinematically into ordered thin disks over the last ~8 billion years since z=1.2, undergoing a process of "disk settling." For the first time, we study the kinematic evolution of a suite of four state of the art "zoom in" hydrodynamic simulations of galaxy formation and evolution in a fully cosmological context and compare with these observations. Until now, robust measurements of the internal kinematics of simulated galaxies were lacking as the simulations suffered from low resolution, overproduction of stars, and overly massive bulges. The current generation of simulations has made great progress in overcoming these difficulties and is ready for a kinematic analysis. We show that simulated galaxies follow the same kinematic trends as real galaxies: they progressively decrease in disordered motions (sigma_g) and increase in ordered rotation (Vrot) with time. The slopes of the relations between both sigma_g and Vrot with redshift are consistent between the simulations and the observations. In addition, the morphologies of the simulated galaxies become less disturbed with time, also consistent with observations, and they both have similarly large scatter. This match between the simulated and observed trends is a significant success for the current generation of simulations, and a first step in determining the physical processes behind disk settling.Comment: ApJ accepted; 6 pages; A pdf with full resolution figures can be found at https://db.tt/8y4Vzaff (2.8M

Incorporating user utility in a smart microgrid with distributed generation and elastic demand.

Demand Side Management (DSM) will play a large role in creating a pathway to a low carbon future. Microgrids are an ideal test bed for DSM within the Smart Grid (SG) framework, allowing for increased integration of distributed generation (DG), here focused on distributed Renewable Energy Sources (RESs). Existing work uses conservative estimates to model the stochastic nature of RESs, resulting in inaccuracies in simulation results. Large uncertainty in user specific participation in DSM programs exists. This paper develops a flexible energy load function, effectively incorporating different user's behaviour patterns into the DSM framework. Uncertainty in connecting small-scale wind generation into the smart microgrid is reduced by using an expected cost function to accurately map predicted wind speed to power output. Actual wind speed is varied across numerous sub-horizons within each time slot by using a pseudo-random number generator. The stochastic nature of renewable generation is effectively managed, producing a robust simulation. Model sensitivities are investigated and graphical results presented