Network models for nonlocal traffic flow

We present a network formulation for a traffic flow model with nonlocal velocity in the flux function. The modeling framework includes suitable coupling conditions at intersections to either ensure maximum flux or distribution parameters. In particular, we focus on 1-to-1, 2-to-1 and 1-to-2 junctions. Based on an upwind type numerical scheme, we prove the maximum principle and the existence of weak solutions on networks. We also investigate the limiting behavior of the proposed models when the nonlocal influence tends to infinity. Numerical examples show the difference between the proposed coupling conditions and a comparison to the Lighthill-Whitham-Richards network model.

Provably non-stiff implementation of weak coupling conditions for hyperbolic problems

In the context of coupling hyperbolic problems, the maximum stable time step of an explicit numerical scheme may depend on the design of the coupling procedure. If this is the case, the coupling procedure is sensitive to changes in model parameters independent of the Courant–Friedrichs–Levy condition. This sensitivity can cause artificial stiffness that degrades the performance of a numerical scheme. To overcome this problem, we present a systematic and general procedure for weakly imposing coupling conditions via penalty terms in a provably non-stiff manner. The procedure can be used to construct both energy conservative and dissipative couplings, and the user is given control over the amount of dissipation desired. The resulting formulation is simple to implement and dual consistent. The penalty coefficients take the form of projection matrices based on the coupling conditions. Numerical experiments demonstrate that this procedure results in both optimal spectral radii and superconvergent linear functionals.

Parity–Time Symmetric Model and Analysis for Stable Multi-Load Wireless Power Transfer

A noticeable challenge for a multi-load wireless power transfer system is to achieve stable power transfer under a dynamic change in coupling conditions. It was proposed that the parity–time symmetric wireless power transfer (PT-WPT) system can achieve stable output efficiency for a single receiver when tuned at the purely real eigenfrequency. However, in the case of higher order, PT symmetric systems usually cannot maintain the real eigenfrequency. To address the issue, a high-order PT-WPT model was established using coupled mode theory (CMT) theory in this paper, and the eigenfrequency of the multi-load PT-WPT system was analyzed. Here, we propose that, theoretically, the system can work at the purely real eigenfrequency by impedance matching. The transfer efficiency of the multi-load PT-WPT system when the system works at the real eigenfrequency was analyzed. The results of the numerical simulation show that the multi load PT-WPT system can maintain stable output efficiency under a dynamic change in coupling conditions. In the long run, our work provides a new possibility for the stable transmission of the multi-load wireless power transfer system.