Conditions implying regularity of the three dimensional Navier-Stokes equation

We obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac like inequalities. As part of the our methods, we give a different approach to a priori estimates of Foias, Guillope and Temam.Comment: Also available at http://www.math.missouri.edu/~stephen/preprints/ (Changes: this is a substantial rewrite of the previous version.

Photovoltaic Emulation System and Maximum Power Point Tracking Algorithm Under Partial Shading Conditions

In this thesis, a novel photovoltaic (PV) emulator and the state-of-art learning–based real-time hybrid maximum power point tracking (MPPT) algorithms have been presented. Real-time research on PV systems is a challenging task because it requires a precise PV emulator that can faithfully reproduce the nonlinear properties of a PV array. The prime objective of the constructed emulator based on integration of unilluminated solar panels with external current sources is to overcome the constraints such as the need for wide surrounding space, high installation cost, and lack of control over the environmental conditions. In addition, the proposed PV emulator is able to simulate the electrical characteristics of the PV system under uniform irradiation as well as partially shading conditions (PSC). Moreover, the application of MPPT technology in PV systems under PSC conditions is challenging. Under complex environmental conditions, the power-voltage (P-V) characteristic curve of a PV system is likely to contain both local global maximum power points (LMPPs) and global maximum power points (GMPP). The MPPT algorithm applied to a PV system should have minimal steady-state oscillations to reduce power losses while accurately searching for the GMPP. The proposed MPPT algorithms resolved the drawbacks of the conventional MPPT method that have poor transient response, high continuous steady-state oscillation, and inefficient tracking performance of maximum power point voltage in the presence of partial shading. The intended algorithms have been verified using MATLAB/Simulink and the proposed PV emulator by applying comparative analysis with the traditional MPPT algorithms. In addition, the performance of the proposed MPPT algorithms and control scheme is validated experimentally with the implementation of MATLAB/Simulink/Stateflow on dSPACE Real-Time-Interface (RTI) 1007 processor board and DS2004 A/D and CP4002 Digital I/O boards. The results indicate that the algorithm is effective in reducing power losses and faster in tracking the speed of the maximum power point with less oscillation under partial shading conditions. In addition, excellent dynamic characteristics of the proposed emulator have been proven to be an ideal tool for testing PV inverters and various maximum power point tracking (MPPT) algorithms for commercial applications and university studies

Networked News Participation: Future Pathways

Civic participation in news production has been a trend under academic scrutiny for at least two decades. The prevalence of digital communication and the dominance of proprietary platforms are two combining forces that disrupt the established journalistic norms. In this article, we investigate news participation and make three grand statements regarding: 1) the holistic definition of participation, 2) the network structure of participation delineating the power dynamics of different media actors, and 3) the transnational context of participation exhibiting the structural constraints within nation-state sovereignty. It is our argument that news participation as a civic act in the digital, globalized age has not fundamentally democratized the information flow as early optimists predicted. Instead, a group of “information elite” have risen to power due to their access to institutional resources, their advantageous positioning in the media ecology, and their entrenchment in the dominant ideology. Participation on proprietary platforms can be easily co-opted to serve the interest of the new information elite

On the blow up criterion for the 2-D compressible Navier-Stokes equations

summary:Motivated by [10], we prove that the upper bound of the density function $\rho$ controls the finite time blow up of the classical solutions to the 2-D compressible isentropic Navier-Stokes equations. This result generalizes the corresponding result in [3] concerning the regularities to the weak solutions of the 2-D compressible Navier-Stokes equations in the periodic domain