In this paper, we introduce and study one-dimensional models for the behavior of pedestrians in a narrow street or corridor. We begin at the microscopic level by formulating a stochastic cellular automata model with explicit rules for pedestrians moving in two opposite directions. Coarse-grained mesoscopic and macroscopic analogs are derived leading to the coupled system of PDEs for the density of the pedestrian traffic. The obtained PDE system is of a mixed hyperbolic-elliptic type and therefore, we rigorously derive higher-order nonlinear diffusive corrections for the macroscopic PDE model. We perform numerical experiments, which compare and contrast the behavior of the microscopic stochastic model and the resulting coarse-grained PDEs for various parameter settings and initial conditions. We also demonstrate that the nonlinear diffusion is essential for reproducing the behavior of the stochastic system in the nonhyperbolic regime.

We first develop non-oscillatory central schemes for a traffic flow model with Arrhenius look-ahead dynamics, proposed in [A. Sopasakis and M.A. Katsoulakis, SIAM J. Appl. Math., 66 (2006), pp. 921-944]. This model takes into account interactions of every vehicle with other vehicles ahead ("look-ahead" rule) and can be written as a one-dimensional scalar conservation law with a global flux. The proposed schemes are extensions of the nonoscillatory central schemes, which belong to a class of Godunov-type projectionevolution methods. In this framework, a solution, computed at a certain time, is first approximated by a piecewise polynomial function, which is then evolved to the next time level according to the integral form of the conservation law. Most Godunov-type schemes are based on upwinding, which requires solving (generalized) Riemann problems. However, no (approximate) Riemann problem solver is available for conservation laws with global fluxes. Therefore, central schemes, which are Riemann-problem-solver-free, are especially attractive for the studied traffic flow model. Our numerical experiments demonstrate high resolution, stability, and robustness of the proposed methods, which are used to numerically investigate both dispersive and smoothing effects of the global flux.We also modify the model by Sopasakis and Katsoulakis by introducing a more realistic, linear interaction potential that takes into account the fact that a car's speed is affected more by nearby vehicles than distant (but still visible) ones. The central schemes are extended to the modified model. Our numerical studies clearly suggest that in the case of a good visibility, the new model yields solutions that seem to better correspond to reality.

No abstract

We employ metamaterial beam-wave interaction structures for tuning the gain and bandwidth of short traveling wave tubes. The interaction structures are made from metal rings of uniform cross section, which are periodically deployed along the length of the traveling wave tube. The aspect ratio of the ring cross sections are adjusted to control both gain and bandwidth. The frequency of operation is controlled by the filling fraction of the ring cross section with respect to the period.

No abstract