Unimodal, concave relationships between average network productivity and accumulation or density aggregated across spatially compact regions of urban networks—so called Macroscopic Fundamental Diagrams (MFDs)—have recently been shown to exist on homogeneous street networks. When present, MFD facilitate the modeling traffic congestion at a regional level have led development various control stra...

Despite the availability of large empirical data sets and the long history of traffic modeling, the theory of traffic congestion on freeways is still highly controversial. In this contribution, we compare Kerner’s three-phase traffic theory with the phase diagram approach for traffic models with a fundamental diagram. We discuss the inconsistent use of the term “traffic phase” and show that pat...

Mitchell JR, Wang J. Expanding application of the Wiggers diagram to teach cardiovascular physiology. Adv Physiol Educ 38: 170–175, 2014; doi:10.1152/advan.00123.2013.—Dr. Carl Wiggers’ careful observations have provided a meaningful resource for students to learn how the heart works. Throughout the many years from his initial reports, the Wiggers diagram has been used, in various degrees of co...

This paper further investigates the specification and calibration of FDs. The purpose is to provide a consistent, systematic, and adaptive way to obtain FDs from single-loop detector measurements. In particular, the piecewise linear form is adopted for the FD, because (a) more-complex forms of the FD can be approximated by a piecewise linear form with arbitrarily many pieces, and (b) empirical ...

Motivated by microscopic traffic modeling, we analyze dynamical systems which have a piecewise linear concave dynamics not necessarily monotonic. We introduce a deterministic Petri net extension where edges may have negative weights. The dynamics of these Petri nets are uniquely defined and may be described by a generalized matrix with a submatrix in the standard algebra with possibly negative ...

We show that an electronic phase separation (EPS) transition described by the Cahn-Hilliard theory yields regions of low free energy forming grains of low and high charge densities. These local differences in the potential energy are studied numerically and used here for the first time as the origin of an attractive interaction that gives rise to local pair formation. The resistivity transition...