Finiteness of cohomology groups of stacks of shtukas as modules over Hecke algebras, and applications

In this paper we prove that the cohomology groups with compact support of stacks of shtukas are modules of finite type over a Hecke algebra. As an application, we extend the construction of excursion operators, defined by V. Lafforgue on the space of cuspidal automorphic forms, to the space of automorphic forms with compact support. This gives the Langlands parametrization for some quotient spaces of the latter, which is compatible with the constant term morphism.Comment: published versio

Cohomology with integral coefficients of stacks of shtukas

We construct the cuspidal cohomology groups of stacks of shtukas with $\mathbb Z_{\ell}$-coefficients and prove that they are $\mathbb Z_{\ell}$-modules of finite type. We prove that the cohomology groups with compact support of stacks of shtukas with $\mathbb Z_{\ell}$-coefficients are modules of finite type over a Hecke algebra with $\mathbb Z_{\ell}$-coefficients. As an application, we prove that the cuspidal cohomology groups with $\mathbb Q_{\ell}$-coefficients are equal to the Hecke-finite cohomology groups with $\mathbb Q_{\ell}$-coefficients defined by V. Lafforgue

High-responsivity vertical-illumination Si/Ge uni-traveling-carrier photodiodes based on silicon-on-insulator substrate

Si/Ge uni-traveling carrier photodiodes exhibit higher output current when space-charge effects are overcome and thermal effects are suppressed, which is highly beneficial for increasing the dynamic range of various microwave photonic systems and simplifying high-bit-rate digital receivers in different applications. From the point of view of packaging, detectors with vertical-illumination configuration can be easily handled by pick-and-place tools and are a popular choice for making photo-receiver modules. However, vertical-illumination Si/Ge uni-traveling carrier (UTC) devices suffer from inter-constraint between high speed and high responsivity. Here, we report a high responsivity vertical-illumination Si/Ge UTC photodiode based on a silicon-on-insulator substrate. The maximum absorption efficiency of the devices was 2.4 times greater than the silicon substrate owing to constructive interference. The Si/Ge UTC photodiode was successfully fabricated and had a dominant responsivity at 1550 nm of 0.18 A/W, a 50% improvement even with a 25% thinner Ge absorption layer.Comment: 5pages,2figure

In-Situ Algae Control Using Water-Lifting Aerators In A Eutrophicated Source Water Reservoir

Algal pollution is a common water quality problem in many source water reservoirs worldwide and directly threatens the safety of drinking water. Water-lifting aeration has been recently developed to improve the source water quality and to control the excessive algae growth by transporting algae from the surface water to the bottom water of the reservoir. Taking the Shibianyu Reservoir supplying 20% source water to Xi’an, China, as a study case, the effect of in-situ algae control using water-lifting aerators was numerically investigated with Fluent. Two submerged water-lifting aerators with different circulation flow rates were installed with different local water depths respectively. Accurate geometry data required for the mesh generation were obtained using a global position system based on real time kinematic technique (V8 Star) and a depth meter (HD 17). The three-dimensional flow velocities were measured with an Acoustic Doppler Profiler (WH600kHz, LAUREL). The water-lifting aerator was simplified as a cylinder and the periodic velocity at the aerator’s outlet was numerically calculated with Euler-Euler multiphase model. The temporal distribution of velocity at the domain inlet, the vertical distributions of initial water temperature and volume fraction of algae, the density and viscosity with water temperature were all imposed with user defined functions written in C programming language. The volume fraction of algae was calculated with the algae content and algae diameter. The algae transport was also simulated with Euler-Euler multiphase model and the turbulence was modeled with RNG model. Before running the aerators, the water temperature decreased from 18℃ at the surface to 16℃ at the water depth of 46m, and to 10℃ at the depth of 50m; the volume fraction of algae increased from 2.0e-3 at the surface to 3.3e-3 at the depth of 5m, decreased to 9.1e-5 at the depth of 15m and then remained constant in the deeper water. At day 10 after operating the aerators, the water temperature became nearly uniform in the reservoir, the algae content in the surface area was greatly decreased, but the algae content in the lower water was increased. Due to its floating velocity of 0.000275m/s, the microcystis aeruginosa, which is the dominant species of algae, was transported to and deposited at zones near the bottom and side wall. The distributions of simulated flow velocity, water temperature and algae content agreed well with the measured ones on the field. Based on the simulation results of algae transport under other characteristic water levels and temperature gradients, the effect of algae control using water-lifting aeration was comprehensively evaluated and the optimized operational conditions were suggested for the reservoir management