On the thermal conduction in tangled magnetic fields in clusters of galaxies

Thermal conduction in tangled magnetic fields is reduced because heat conducting electrons must travel along the field lines longer distances between hot and cold regions of space than if there were no fields. We consider the case when the tangled magnetic field has a weak homogeneous component. We examine two simple models for temperature in clusters of galaxies: a time-independent model and a time-dependent one. We find that the actual value of the effective thermal conductivity in tangled magnetic fields depends on how it is defined for a particular astrophysical problem. Our final conclusion is that the heat conduction never totally suppressed but is usually important in the central regions of galaxy clusters, and therefore, it should not be neglected.Comment: 16 pages, 4 figure

A Link-based Mixed Integer LP Approach for Adaptive Traffic Signal Control

This paper is concerned with adaptive signal control problems on a road network, using a link-based kinematic wave model (Han et al., 2012). Such a model employs the Lighthill-Whitham-Richards model with a triangular fundamental diagram. A variational type argument (Lax, 1957; Newell, 1993) is applied so that the system dynamics can be determined without knowledge of the traffic state in the interior of each link. A Riemann problem for the signalized junction is explicitly solved; and an optimization problem is formulated in continuous-time with the aid of binary variables. A time-discretization turns the optimization problem into a mixed integer linear program (MILP). Unlike the cell-based approaches (Daganzo, 1995; Lin and Wang, 2004; Lo, 1999b), the proposed framework does not require modeling or computation within a link, thus reducing the number of (binary) variables and computational effort. The proposed model is free of vehicle-holding problems, and captures important features of signalized networks such as physical queue, spill back, vehicle turning, time-varying flow patterns and dynamic signal timing plans. The MILP can be efficiently solved with standard optimization software.Comment: 15 pages, 7 figures, current version is accepted for presentation at the 92nd Annual Meeting of Transportation Research Boar