Macroscopic Dynamics of Multi-Lane Traffic

We present a macroscopic model of mixed multi-lane freeway traffic that can be easily calibrated to empirical traffic data, as is shown for Dutch highway data. The model is derived from a gas-kinetic level of description, including effects of vehicular space requirements and velocity correlations between successive vehicles. We also give a derivation of the lane-changing rates. The resulting dynamic velocity equations contain non-local and anisotropic interaction terms which allow a robust and efficient numerical simulation of multi-lane traffic. As demonstrated by various examples, this facilitates the investigation of synchronization patterns among lanes and effects of on-ramps, off-ramps, lane closures, or accidents.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

The life cycle impact for platinum group metals and lithium to 2070 via surplus cost potential

© 2017 The Author(s)Purpose: A surplus cost potential (SCP) indicator has been developed as a measure of resource scarcity in the life cycle impact assessment (LCIA) context. To date, quality SCP estimates for other minerals than fossils are either not yet available or suffer methodological and data limitations. This paper overcomes these limitations and demonstrate how SCP estimates for metals can be calculated without the utilisation of ore grade function and by collecting primary economic and geological data. Methods: Data were collected in line with the geographical distribution, mine type, deposit type and production volumes and total production costs in order to construct cost-cumulative availability curves for platinum group metals (PGMs) and lithium. These curves capture the total amount of known mineral resources that can be recovered profitably at various prices from different types of mineral deposits under current conditions (this is, current technology, prevailing labour and other input prices). They served as a basis for modelling the marginal cost increase, a necessary parameter for estimating the SCP indicator. Surplus costs were calculated for different scenario projections for future mineral production considering future market dynamics, recyclability rates, demand-side technological developments and economic growth and by applying declining social discount rate. Results and discussion: Surplus costs were calculated for three mineral production scenarios, ranging from (US$2014/kg) 6545–8354 for platinum, 3583–4573 for palladium, 8281–10,569 for rhodium, 513–655 for ruthenium, 3201–4086 for iridium and 1.70–5.80 for lithium. Compared with the current production costs, the results indicate that problematic price increases of lithium are unlikely if the latest technological trends in the automotive sector will continue up to 2070. Surplus costs for PGMs are approximately one-third of the current production costs in all scenarios; hence, a threat of their price increases by 2070 will largely depend on the discovery of new deposits and the ability of new technologies to push these costs down over time. This also applies to lithium if the increasing electrification of road transport will continue up to 2070. Conclusions: This study provides useful insight into the availability of PGMs and lithium up to 2070. It proves that if time and resources permit, reliable surplus cost estimates can be calculated, at least in the short-run, based on the construction of one’s own curves with the level of quality comparable to expert-driven consulting services. Modelling and incorporating unknown deposits and potential future mineral production costs into these curves is the subject of future work

Traffic and Related Self-Driven Many-Particle Systems

Since the subject of traffic dynamics has captured the interest of physicists, many astonishing effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by so-called ``phantom traffic jams'', although they all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction of the traffic volume cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize in lanes, while similar systems are ``freezing by heating''? Why do self-organizing systems tend to reach an optimal state? Why do panicking pedestrians produce dangerous deadlocks? All these questions have been answered by applying and extending methods from statistical physics and non-linear dynamics to self-driven many-particle systems. This review article on traffic introduces (i) empirically data, facts, and observations, (ii) the main approaches to pedestrian, highway, and city traffic, (iii) microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts like a general modelling framework for self-driven many-particle systems, including spin systems. Subjects such as the optimization of traffic flows and relations to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are discussed as well.Comment: A shortened version of this article will appear in Reviews of Modern Physics, an extended one as a book. The 63 figures were omitted because of storage capacity. For related work see http://www.helbing.org