Large-Time Behavior of the 2D Compressible Navier-Stokes System in Bounded Domains with Large Data and Vacuum

The large time behavior of the unique strong solution to the barotropic compressible Navier-Stokes system is studied with large external forces and initial data, where the shear viscosity is a positive constant and the bulk one is proportional to a power of the density. Some uniform estimates on the Lp-norm of the density are established, and then deduce that the density converges to its steady state in Lp-spaces, which transforms the large external force into a small one in some sense. Moreover, to deal with the obstacles brought by boundary, the conformal mapping and the pull back Green function are applied to give a point-wise representation of the effective viscous flux, and then make use of slip boundary conditions to cancel out the singularity.Comment: 55 page

Intrusions into Privacy in Video Chat Environments: Attacks and Countermeasures

Video chat systems such as Chatroulette have become increasingly popular as a way to meet and converse one-on-one via video and audio with other users online in an open and interactive manner. At the same time, security and privacy concerns inherent in such communication have been little explored. This paper presents one of the first investigations of the privacy threats found in such video chat systems, identifying three such threats, namely de-anonymization attacks, phishing attacks, and man-in-the-middle attacks. The paper further describes countermeasures against each of these attacks.Comment: 8 pages, submitted to WPE

Impact of Water Mixing and Ice Formation on the Warming of Lake Superior: A Model-guided Mechanism Study

The Laurentian Great Lakes are one of the most prominent hotspots for the study of climate change induced lake warming. Warming trends in large, deep lakes, which are often inferred by the observations of lake surface temperature (LST) in most studies, are strongly linked to the total lake heat content. In this study, we use a 3D hydrodynamic model to examine the nonlinear processes of water mixing and ice formation that cause changes in lake heat content and further variation of LST. With a focus on mechanism study, a series of process-oriented experiments is carried out to understand the interactions among these processes and their relative importance to the lake heat budget. Using this hydrodynamic model, we estimate the lake heat content by integrating over the entire 3D volume. Our analysis reveals that (1) Heat content trends do not necessarily follow (can even be opposed to) trends in LST. Hence, using LST as a warming indicator can be problematic; (2) vertical mixing in water column may play a more important role in regulating lake warming than traditionally expected. Changes in the water mixing pattern can have a prolonged effect on the thermal structure; (3) Ice albedo feedback, even in cold winters, has little impact on lake thermal structure, and its influence on lake warming may have been overestimated. Our results indicate that climate change will not only affect the air-lake energy exchange but can also alter lake internal dynamics, therefore, the lake\u27s response to a changing climate may vary with time

A hybrid lagrangian–eulerian particle model for ecosystem simulation

Current numerical methods for simulating biophysical processes in aquatic environments are typically constructed in a grid-based Eulerian framework or as an individual-based model in a particle-based Lagrangian framework. Often, the biogeochemical processes and physical (hydrodynamic) processes occur at different time and space scales, and changes in biological processes do not affect the hydrodynamic conditions. Therefore, it is possible to develop an alternative strategy to grid-based approaches for linking hydrodynamic and biogeochemical models that can significantly improve computational efficiency for this type of linked biophysical model. In this work, we utilize a new technique that links hydrodynamic effects and biological processes through a property-carrying particle model (PCPM) in a Lagrangian/Eulerian framework. The model is tested in idealized cases and its utility is demonstrated in a practical application to Sandusky Bay. Results show the integration of Lagrangian and Eulerian approaches allows for a natural coupling of mass transport (represented by particle movements and random walk) and biological processes in water columns which is described by a nutrient-phytoplankton-zooplankton-detritus (NPZD) biological model. This method is far more efficient than traditional tracer-based Eulerian biophysical models for 3-D simulation, particularly for a large domain and/or ensemble simulations