Construction of vacuum initial data by the conformally covariant split system

Using the implicit function theorem, we prove existence of solutions of the so-called conformally covariant split system on compact 3-dimensional Riemannian manifolds. They give rise to non-Constant Mean Curvature (non-CMC) vacuum initial data for the Einstein equations. We investigate the conformally covariant split system defined on compact manifolds with or without boundaries. In the former case, the boundary corresponds to an apparent horizon in the constructed initial data. The case with a cosmological constant is then considered separately. Finally, to demonstrate the applicability of the conformal covariant split system in numerical studies, we provide numerical examples of solutions on manifolds $\mathbb S^1 \times \mathbb S^2$ and $\mathbb S^1 \times \mathbb T^2$

On Hawking mass and Bartnik mass of CMC surfaces

Given a constant mean curvature surface that bounds a compact manifold with nonnegative scalar curvature, we obtain intrinsic conditions on the surface that guarantee the positivity of its Hawking mass. We also obtain estimates of the Bartnik mass of such surfaces, without assumptions on the integral of the squared mean curvature. If the ambient manifold has negative scalar curvature, our method also applies and yields estimates on the hyperbolic Bartnik mass of these surfaces.Comment: version accepted by Math. Res. Let

An in-depth analysis of system-level techniques for Simultaneous Multi-threaded Processors in Clouds

To improve the overall system utilization, Simultaneous Multi-Threading (SMT) has become a norm in clouds. Usually, Hardware threads are viewed and deployed directly as physical cores for attempts to improve resource utilization and system throughput. However, context switches in virtualized systems might incur severe resource waste, which further led to significant performance degradation. Worse, virtualized systems suffer from performance variations since the rescheduled vCPU may affect other hardware threads on the same physical core. In this paper, we perform an in-depth experimental study about how existing system software techniques improves the utilization of SMT Processors in Clouds. Considering the default Linux hypervisor vanilla KVM as the baseline, we evaluated two update-to-date kernel patches IdlePoll and HaltPoll through the combination of 14 real-world workloads. Our results show that mitigating they could significantly mitigate the number of context switches, which further improves the overall system throughput and decreases its latency. Based on our findings, we summarize key lessons from the previous wisdom and then discuss promising directions to be explored in the future