This survey summarizes and illustrates the main qualitative properties of hydrodynamics models for collective behavior. These models include a velocity consensus term together with attractive-repulsive potentials leading to non-trivial flock profiles. The connection between the underlying particle systems to the swarming hydrodynamic equations is performed through kinetic theory modelling arguments. We focus on Lagrangian schemes for the hydrodynamic systems showing the different qualitative behavior of the systems and its capability of keeping properties of the original particle models. We illustrate known results concerning large time profiles and blow-up in finite time of the hydrodynamic systems to validate the numerical scheme. We finally explore unknown situations making use of the numerical scheme showcasing a number of conjectures based on the numerical results.

The New York State Mesonet (NYSM) is a network of 126 standard environmental monitoring stations deployed statewide with an average spacing of 27 km. The primary goal of the NYSM is to provide high quality weather data at high spatial and temporal scales to improve atmospheric monitoring and prediction, especially for extreme weather events. Compared with other statewide networks, the NYSM faced considerable deployment obstacles with New York’s complex terrain, forests, and very rural and urban areas; its wide range of weather extremes; and its harsh winter conditions. To overcome these challenges, the NYSM adopted a number of innovations unique among statewide monitoring systems, including: (1) Strict adherence to international siting standards and metadata documentation; (2) A hardened system design to facilitate continued operations during extreme, high-impact weather; (3) A station design optimized to monitor winter weather conditions; and (4) a camera installed at every site to aid situational awareness. Completed in spring 2018, the network provides data and products to a variety of sectors including weather monitoring and forecasting, emergency management, agriculture, transportation, utilities, and education. This paper focuses on the standard network of the NYSM and reviews the network siting, site configuration, sensors, site communications and power, network operations and maintenance, data quality control, and dissemination. A few example analyses are shown which highlight the benefits of the NYSM.

No abstract

In this work we introduce a finite-volume numerical scheme for solving stochastic gradient flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed scheme deals with general free-energy functionals, including, for instance, external fields or interaction potentials. This allows us to simulate a range of physical phenomena where thermal fluctuations play a crucial role, such as nucleation and further energy-barrier crossing transitions. A positivity-preserving algorithm for the density is derived based on a hybrid space discretization of the deterministic and the stochastic terms and different implicit and explicit time integrators. We show through numerous applications that not only our scheme is able to accurately reproduce the statistical properties (structure factor and correlations) of the physical system, but, because of the multiplicative noise, it allows us to simulate energy barrier crossing dynamics, which cannot be captured by mean field approaches.